Trigonometry

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What are the primary trigonometric ratios?

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Sine, cosine, and tangent.

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What are the primary trigonometric ratios?

Sine, cosine, and tangent.

How is sine defined in a right-angled triangle?

$	ext{Sine} = rac{	ext{Opposite}}{	ext{Hypotenuse}}$.

What is the formula for cosine in a right-angled triangle?

$	ext{Cosine} = rac{	ext{Adjacent}}{	ext{Hypotenuse}}$.

What is the tangent ratio?

$	an(	heta) = rac{	ext{Opposite}}{	ext{Adjacent}} = rac{	ext{Sine}}{	ext{Cosine}}$.

What are the reciprocal trigonometric ratios?

Cosecant, secant, and cotangent.

How is cosecant defined?

$	ext{Cosecant} = rac{1}{	ext{Sine}}$.

What is the Pythagorean identity for sine and cosine?

$	ext{sin}^2(	heta) + 	ext{cos}^2(	heta) = 1$.

What is the angle sum identity for sine?

$	ext{sin}(	heta_1 	ext{+} 	heta_2) = 	ext{sin}(	heta_1)	ext{cos}(	heta_2) + 	ext{cos}(	heta_1)	ext{sin}(	heta_2)$.

What is the double angle identity for sine?

$	ext{sin}(2	heta) = 2	ext{sin}(	heta)	ext{cos}(	heta)$.

What are the principal values of $	ext{sin}^{-1}(x)$?

$[-rac{	ext{π}}{2}, rac{	ext{π}}{2}]$.

What is the period of the sine and cosine functions?

$2	ext{π}$.

Where do the vertical asymptotes of the tangent function occur?

At $x = rac{	ext{π}}{2} + n	ext{π}$, where $n$ is an integer.

How do you solve basic trigonometric equations?

Use inverse functions and consider periodicity.

What is the inequality for sine?

To solve $	ext{sin}(x) > a$, use the unit circle.

What is the definition of cosine in a right-angled triangle?

$	ext{Cosine} = rac{	ext{Adjacent}}{	ext{Hypotenuse}}$.

What is the formula for tangent in terms of sine and cosine?

$	an(	heta) = rac{	ext{sin}(	heta)}{	ext{cos}(	heta)}$.

What is the relationship between cotangent and tangent?

$	ext{cot}(	heta) = rac{1}{	an(	heta)} = rac{	ext{cos}(	heta)}{	ext{sin}(	heta)}$.

What is the identity for $	an(	heta)$ in terms of sine and cosine?

$	an(	heta) = rac{	ext{sin}(	heta)}{	ext{cos}(	heta)}$.

What is the identity for $	ext{sec}(	heta)$?

$	ext{sec}(	heta) = rac{1}{	ext{cos}(	heta)}$.

What is the identity for $	ext{csc}(	heta)$?

$	ext{csc}(	heta) = rac{1}{	ext{sin}(	heta)}$.

1 / 20

What are the primary trigonometric ratios?

Flip

Spacebar

Sine, cosine, and tangent.

Flip

Spacebar

What are the primary trigonometric ratios?

Sine, cosine, and tangent.

How is sine defined in a right-angled triangle?

$	ext{Sine} = rac{	ext{Opposite}}{	ext{Hypotenuse}}$.

What is the formula for cosine in a right-angled triangle?

$	ext{Cosine} = rac{	ext{Adjacent}}{	ext{Hypotenuse}}$.

What is the tangent ratio?

$	an(	heta) = rac{	ext{Opposite}}{	ext{Adjacent}} = rac{	ext{Sine}}{	ext{Cosine}}$.

What are the reciprocal trigonometric ratios?

Cosecant, secant, and cotangent.

How is cosecant defined?

$	ext{Cosecant} = rac{1}{	ext{Sine}}$.

What is the Pythagorean identity for sine and cosine?

$	ext{sin}^2(	heta) + 	ext{cos}^2(	heta) = 1$.

What is the angle sum identity for sine?

$	ext{sin}(	heta_1 	ext{+} 	heta_2) = 	ext{sin}(	heta_1)	ext{cos}(	heta_2) + 	ext{cos}(	heta_1)	ext{sin}(	heta_2)$.

What is the double angle identity for sine?

$	ext{sin}(2	heta) = 2	ext{sin}(	heta)	ext{cos}(	heta)$.

What are the principal values of $	ext{sin}^{-1}(x)$?

$[-rac{	ext{π}}{2}, rac{	ext{π}}{2}]$.

What is the period of the sine and cosine functions?

$2	ext{π}$.

Where do the vertical asymptotes of the tangent function occur?

At $x = rac{	ext{π}}{2} + n	ext{π}$, where $n$ is an integer.

How do you solve basic trigonometric equations?

Use inverse functions and consider periodicity.

What is the inequality for sine?

To solve $	ext{sin}(x) > a$, use the unit circle.

What is the definition of cosine in a right-angled triangle?

$	ext{Cosine} = rac{	ext{Adjacent}}{	ext{Hypotenuse}}$.

What is the formula for tangent in terms of sine and cosine?

$	an(	heta) = rac{	ext{sin}(	heta)}{	ext{cos}(	heta)}$.

What is the relationship between cotangent and tangent?

$	ext{cot}(	heta) = rac{1}{	an(	heta)} = rac{	ext{cos}(	heta)}{	ext{sin}(	heta)}$.

What is the identity for $	an(	heta)$ in terms of sine and cosine?

$	an(	heta) = rac{	ext{sin}(	heta)}{	ext{cos}(	heta)}$.

What is the identity for $	ext{sec}(	heta)$?

$	ext{sec}(	heta) = rac{1}{	ext{cos}(	heta)}$.

What is the identity for $	ext{csc}(	heta)$?

$	ext{csc}(	heta) = rac{1}{	ext{sin}(	heta)}$.