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devlian [24]
3 years ago
12

-The terminal side of the angle contains the following point. Find the values of the six trigonometric functions for the followi

ng points. #16
-Given the following, state the six trigonometric ratios. #17 #18​

Mathematics
1 answer:
bearhunter [10]3 years ago
4 0

Answer: see attachments

<u>Step-by-step explanation:</u>

Use Pythagorean Theorem to find the missing side (x² + y² = h²)

Use the following formulas to find the trig functions:

sin\theta=\dfrac{y}{h}\qquad \qquad csc\theta=\dfrac{h}{y}\\\\\\cos\theta=\dfrac{x}{h}\qquad \qquad sec\theta=\dfrac{h}{x}\\\\\\tan\theta=\dfrac{y}{x}\qquad \qquad cot\theta=\dfrac{x}{y}

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By using trigonometric relations, we will see that:

AC = 15.6 in

AB = 8.4 in.

<h3>How to get the measures of the other two sides of the right triangle?</h3>

Here we have the right triangle where:

B = 90°

C = 40°

BC = 10 in.

Notice that is the adjacent cathetus to the angle C, then we can use the two relations:

  • sin(a) = (adjacent cathetus)/(hypotenuse).
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Where:

  • hypotenuse = AC
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Then we will have:

sin(40°) = 10in/AC.

AC = 10in/sin(40°) = 15.6 in

tan(40°) = AB/10in

tan(40°)*10in = AB = 8.4 in.

So we can conclude that for the given right triangle we have:

AC = 15.6 in

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If you want to learn more about right triangles:

brainly.com/question/2217700

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2 years ago
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3 years ago
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Answer:

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Step-by-step explanation:

Okay, so to go from a fraction to a decimal, you really just have to put the dot in the right place:

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So 1/6 is 0.167 as a decimal

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