Chapter 8: Q. 10 (page 516)

Find the exact value of the six trigonometric functions of the angle $θ$ in each figure.

Short Answer

Expert verified

The solution is $\sin θ = \frac{3}{5}, \cos θ = \frac{4}{5}, \tan θ = \frac{3}{4}, c s c θ = \frac{5}{3}, s e c θ = \frac{5}{4}, c o t θ = \frac{4}{3}$

Step by step solution

Step 1. Given information

Adjacent $= 4$ and opposite $= 3$

Step 2. Calculation

Let $a = 4$ , $b = 3$ and role="math" localid="1647102231651" $c =$ hypotenuse.

Now, role="math" localid="1647102404943" $c^{2} = a^{2} + b^{2}$ Pythagorean Theorem

$\sqrt{c^{2}} = \sqrt{4^{2} + 3^{2}}$

$c = \sqrt{16 + 9}$

$c = \sqrt{25}$

$c = 5$

Step 3. Calculation

The value of each of the six trigonometric functions are -
$\sin θ = \frac{b}{c} = \frac{3}{5}$ $\cos θ = \frac{a}{c} = \frac{4}{5}$ $\tan θ = \frac{b}{a} = \frac{3}{4}$

$c s c θ = \frac{c}{b} = \frac{5}{3}$ $s e c θ = \frac{c}{a} = \frac{5}{4}$ $c o t θ = \frac{a}{b} = \frac{4}{3}$

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Find the exact value of the six trigonometric functions of the angle $θ$ in each figure.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

Step 3. Calculation

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Find the exact value of the six trigonometric functions of the angle θin each figure.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

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Study anywhere. Anytime. Across all devices.

Find the exact value of the six trigonometric functions of the angle $θ$ in each figure.