Trigonometric Functions and Applications

The video tutorial demonstrates how to use trigonometric equations to determine the length of sides in a right triangle. It covers three examples using sine, cosine, and tangent functions with angles of 34, 56, and 71 degrees, respectively. The tutorial explains how to set up proportions, cross-multiply, and solve for unknown sides using a calculator, ensuring the calculator is in degree mode. Each example highlights the relationship between the angle and the sides of the triangle, providing a step-by-step guide to solving the equations.

What trigonometric function is used when you have the opposite side and the hypotenuse?

• Tangent

• Cosine

• Secant

• Sine

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In the first example, what is the ratio set up for the sine function?

• X to 34

• 34 to X

• X to 27

• 27 to X

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CCSS.HSG.SRT.C.8

If the angle is 34 degrees and the hypotenuse is 27 inches, what is the approximate length of the opposite side?

• 10.5 inches

• 20.3 inches

• 18.7 inches

• 15.1 inches

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What is the first step to ensure your calculator is ready for trigonometric calculations?

• Set to radian mode

• Set to degree mode

• Clear memory

• Turn off

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CCSS.HSG.SRT.C.6

Which trigonometric function involves the adjacent side and the hypotenuse?

• Tangent

• Sine

• Cosecant

• Cosine

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CCSS.HSG.SRT.D.11

In the second example, what is the approximate length of the side when using the cosine function with a 56-degree angle?

• 16 meters

• 28.6 meters

• 22.4 meters

• 30.1 meters

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CCSS.HSG.SRT.C.8

What is the purpose of cross-multiplying in these trigonometric problems?

• To find the angle

• To solve for X

• To check the mode

• To find the hypotenuse

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CCSS.HSG.SRT.C.6

What trigonometric function is used when you have the opposite side and the adjacent side?

• Sine

• Cosine

• Tangent

• Cotangent

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CCSS.HSG.SRT.C.8

For a 71-degree angle, if the adjacent side is 5 cm, what is the approximate length of the opposite side?

• 12.3 cm

• 14.5 cm

• 10.2 cm

• 16.7 cm

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CCSS.HSG.SRT.C.8

In the tangent function example, what is the given angle?

• 34 degrees

• 56 degrees

• 71 degrees

• 90 degrees

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