Exploring Right Triangle Trigonometry

The video tutorial explores the concept of triangles outside of circles and how to apply trigonometric ratios to these triangles. It covers the definitions of sine, cosine, and tangent, as well as their reciprocal functions: cosecant, secant, and cotangent. The mnemonic SOH-CAH-TOA is introduced to help remember these ratios. The tutorial also explains how to label the sides of a triangle as opposite, adjacent, and hypotenuse, and demonstrates solving problems to find unknown side lengths using trigonometry.

Why do we need new terminology for triangles that are not on the coordinate plane?

• Because triangles outside the coordinate plane are different shapes.

• Because we no longer have x and y coordinates to refer to.

• Because the triangles are no longer right-angled.

• Because the triangles are inside circles.

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CCSS.2.G.A.1

What is the reciprocal of sine?

• Secant

• Tangent

• Cotangent

• Cosecant

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CCSS.HSG.SRT.C.7

In the context of a right triangle, what does the term 'adjacent' refer to?

• The radius

• The side next to the angle

• The hypotenuse

• The side opposite the angle

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CCSS.HSG.SRT.C.6

What does the mnemonic SOH-CAH-TOA help you remember?

• The Pythagorean theorem

• The types of triangles

• The trigonometric ratios

• The properties of circles

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CCSS.HSG.SRT.C.6

What is the formula for cosine according to SOH-CAH-TOA?

• Adjacent over Hypotenuse

• Opposite over Hypotenuse

• Opposite over Adjacent

• Hypotenuse over Adjacent

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CCSS.HSG.SRT.C.6

If angle A is in a right triangle, what is the sine of angle A?

• Hypotenuse over Opposite

• Adjacent over Opposite

• Opposite over Hypotenuse

• Adjacent over Hypotenuse

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CCSS.HSG.SRT.C.6

In a right triangle, if angle B is given, what is the cosine of angle B?

• Opposite over Hypotenuse

• Adjacent over Hypotenuse

• Hypotenuse over Adjacent

• Opposite over Adjacent

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CCSS.HSG.SRT.C.6

To find the length of side 'a' in a right triangle with a given angle and opposite side, which trigonometric ratio would you use?

• Tangent

• Cosine

• Secant

• Sine

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CCSS.HSG.SRT.C.6

If you know the opposite side and need to find the hypotenuse, which trigonometric function would you use?

• Sine

• Cosine

• Cotangent

• Tangent

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CCSS.HSG.SRT.C.6

What is the approximate value of side 'a' if the opposite side is 10 and the angle is 62 degrees?

• 11.33

• 10.62

• 5.31

• 1.88

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CCSS.HSG.SRT.C.8