Trig Ratios: SOHCAHTOA

Front

What does SOHCAHTOA stand for in trigonometry?

Back

SOHCAHTOA is a mnemonic for remembering the definitions of the sine, cosine, and tangent ratios: Sine = Opposite/Hypotenuse (SOH), Cosine = Adjacent/Hypotenuse (CAH), Tangent = Opposite/Adjacent (TOA).

Tags

CCSS.HSG.SRT.C.6

Front

Define the sine ratio in a right triangle.

Back

The sine ratio is the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is defined as: sin(θ) = Opposite/Hypotenuse.

Tags

CCSS.HSG.SRT.C.6

Front

Define the cosine ratio in a right triangle.

Back

The cosine ratio is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. It is defined as: cos(θ) = Adjacent/Hypotenuse.

Tags

CCSS.HSG.SRT.C.6

Front

Define the tangent ratio in a right triangle.

Back

The tangent ratio is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. It is defined as: tan(θ) = Opposite/Adjacent.

Tags

CCSS.HSG.SRT.C.6

Front

If the opposite side is 3 and the hypotenuse is 5, what is the sine of the angle?

Back

sin(θ) = Opposite/Hypotenuse = 3/5 = 0.6.

Tags

CCSS.HSG.SRT.C.6

Front

If the adjacent side is 4 and the hypotenuse is 5, what is the cosine of the angle?

Back

cos(θ) = Adjacent/Hypotenuse = 4/5 = 0.8.

Tags

CCSS.HSG.SRT.C.6

Front

If the opposite side is 3 and the adjacent side is 4, what is the tangent of the angle?

Back

tan(θ) = Opposite/Adjacent = 3/4 = 0.75.

Tags

CCSS.HSG.SRT.C.6

Front

How do you find the missing side using the sine ratio?

Back

To find the missing side using the sine ratio, rearrange the formula: Opposite = Hypotenuse * sin(θ).

Tags

CCSS.HSG.SRT.C.8

Front

How do you find the missing side using the cosine ratio?

Back

To find the missing side using the cosine ratio, rearrange the formula: Adjacent = Hypotenuse * cos(θ).

Tags

CCSS.HSG.SRT.C.8

Front

How do you find the missing side using the tangent ratio?

Back

To find the missing side using the tangent ratio, rearrange the formula: Opposite = Adjacent * tan(θ).

Tags

CCSS.HSG.SRT.C.8