Right-Triangle Trigonometry flashcards

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Choose a ratio to recover a sideSine, Cosine, and Tangent: Choose the ratio that connects the two sides you actually have.
When should I use sine and cosine?Sine, Cosine, and Tangent: Identify the correct side ratio for an acute right-triangle angle.
What method supports choose a ratio to recover a side?Sine, Cosine, and Tangent: opposite=hypotenuse·sin θ
TangentSine, Cosine, and Tangent: Tangent compares the legs directly.
Sine and cosineSine, Cosine, and Tangent: Sine uses the far leg; cosine uses the near leg.
What must I check in sine, cosine, and tangent?Sine, Cosine, and Tangent: Define opposite and adjacent relative to the selected acute angle; the hypotenuse is always opposite 90°
What method supports tangent?Sine, Cosine, and Tangent: tan θ=opposite/adjacent
What method supports sine and cosine?Sine, Cosine, and Tangent: sin θ=opposite/hypotenuse; cos θ=adjacent/hypotenuse
When should I use choose a ratio to recover a side?Sine, Cosine, and Tangent: Select sine, cosine, or tangent using the known and requested sides.
When should I use tangent?Sine, Cosine, and Tangent: Use the ratio of the two legs.
Angle recovery and modeFinding Missing Sides and Angles: Inverse trig asks which angle has that ratio.
When should I use missing leg from an exact angle?Finding Missing Sides and Angles: Use an exact trigonometric ratio to find a side.
What method supports angle recovery and mode?Finding Missing Sides and Angles: θ=arctan(opposite/adjacent), 0°<θ<90°
Missing hypotenuseFinding Missing Sides and Angles: The longest side must be larger, so divide by the leg fraction.
Missing leg from an exact angleFinding Missing Sides and Angles: An exact angle can give an exact side multiplier.
What must I check in finding missing sides and angles?Finding Missing Sides and Angles: Use degree mode for degree angles and radian mode for radian angles; inverse-trig angle recovery is a supporting extension
What method supports missing hypotenuse?Finding Missing Sides and Angles: hypotenuse=adjacent/cos θ
What method supports missing leg from an exact angle?Finding Missing Sides and Angles: sin30°=1/2; cos60°=1/2
When should I use angle recovery and mode?Finding Missing Sides and Angles: Use an inverse function or a standard exact ratio to find an angle.
When should I use missing hypotenuse?Finding Missing Sides and Angles: Divide by the known side-to-hypotenuse ratio.
Recover a complementary ratioComplementary Angles and Trigonometric Relationships: Use the complementary relationship before reaching for an inverse calculator.
When should I use complementary acute angles?Complementary Angles and Trigonometric Relationships: Recover the other acute angle in a right triangle.
What method supports recover a complementary ratio?Complementary Angles and Trigonometric Relationships: sin²θ+cos²θ=1; cosβ=sinα when α+β=90°
Cofunction ratiosComplementary Angles and Trigonometric Relationships: Sine of one corner is cosine of the other.
Complementary acute anglesComplementary Angles and Trigonometric Relationships: The two sharp corners split a right angle.
What must I check in complementary angles and trigonometric relationships?Complementary Angles and Trigonometric Relationships: The cofunction identities pair angles summing to 90°; do not confuse them with equal-angle claims
What method supports cofunction ratios?Complementary Angles and Trigonometric Relationships: sin θ=cos(90°−θ)
What method supports complementary acute angles?Complementary Angles and Trigonometric Relationships: α+β=90°
When should I use recover a complementary ratio?Complementary Angles and Trigonometric Relationships: Translate a known ratio to the complementary angle.
When should I use cofunction ratios?Complementary Angles and Trigonometric Relationships: Use a sine-cosine complement identity.
Quadrants and reference anglesDegrees, Radians, and Relevant Unit-Circle Relationships: Find the reference angle and then apply the quadrant signs.
When should I use degree-radian conversion?Degrees, Radians, and Relevant Unit-Circle Relationships: Convert angle measures with π radians equal to 180°.
What method supports quadrants and reference angles?Degrees, Radians, and Relevant Unit-Circle Relationships: cos(180°−α)=−cosα; sin(180°−α)=sinα
Unit-circle coordinatesDegrees, Radians, and Relevant Unit-Circle Relationships: Cosine is left-right; sine is up-down.
Degree-radian conversionDegrees, Radians, and Relevant Unit-Circle Relationships: Use 180° and π radians as equal measures.
What must I check in degrees, radians, and relevant unit-circle relationships?Degrees, Radians, and Relevant Unit-Circle Relationships: A full revolution is 2π radians or 360°; unit-circle coordinates are (cosθ,sinθ) and quadrant signs matter
What method supports unit-circle coordinates?Degrees, Radians, and Relevant Unit-Circle Relationships: (x,y)=(cosθ,sinθ), x²+y²=1
What method supports degree-radian conversion?Degrees, Radians, and Relevant Unit-Circle Relationships: radians=degrees·π/180
When should I use quadrants and reference angles?Degrees, Radians, and Relevant Unit-Circle Relationships: Use a reference angle and signs to find an exact trig value.
When should I use unit-circle coordinates?Degrees, Radians, and Relevant Unit-Circle Relationships: Connect sine and cosine to horizontal and vertical coordinates.
Sloped path and vertical riseTrigonometric Word Problems: A sloped length is the longest side, so choose sine for the rise.
When should I use angle of elevation?Trigonometric Word Problems: Relate vertical rise and horizontal distance with tangent.
What method supports sloped path and vertical rise?Trigonometric Word Problems: vertical rise=sloped length·sinθ
Observer heightTrigonometric Word Problems: The trig triangle starts at eye level, so add that level back.
Angle of elevationTrigonometric Word Problems: Elevation connects height above the sightline to horizontal distance.
What must I check in trigonometric word problems?Trigonometric Word Problems: Assume level ground and vertical objects only when stated; add observer height separately from the triangle’s vertical rise
What method supports observer height?Trigonometric Word Problems: object height=instrument height+d·tanθ
What method supports angle of elevation?Trigonometric Word Problems: rise=horizontal distance·tanθ
When should I use sloped path and vertical rise?Trigonometric Word Problems: Use sine when the known distance is a hypotenuse.
When should I use observer height?Trigonometric Word Problems: Add instrument height after finding the vertical rise.