Chapter 8: Q. 1 (page 555)

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

Short Answer

Expert verified

The ratio are,

$\sin θ = \frac{\sqrt{5}}{5} \cos θ = \frac{2 \sqrt{5}}{5} \tan θ = \frac{1}{2} co t θ = 2 c s c θ = \sqrt{5} s e c θ = \frac{\sqrt{5}}{2}$

Step by step solution

Step 1. Given Information

The given triangle is,

Step 2. Determine the hypotenuse

In the given triangle, $p = 3, b = 6$ .
Use Pythagoras theorem, to determine the hypotenuse.

role="math" localid="1646825617277" $\begin{array}{rcl} h^{2} & = & p^{2} + b^{2} \\ h^{2} & = & 3^{2} + 6^{2} \\ h^{2} & = & 9 + 36 \\ h & = & \sqrt{45} \\ = & 3 \sqrt{5} \end{array}$

Step 3. Determine the trigonometric ratios.

Determine the trigonometric ratios.

$\sin θ = \frac{p}{h} = \frac{3}{3 \sqrt{5}} = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5} \cos θ = \frac{b}{h} = \frac{6}{3 \sqrt{5}} = \frac{2}{\sqrt{5}} = \frac{2 \sqrt{5}}{5} \tan θ = \frac{p}{b} = \frac{3}{6} = \frac{1}{2} co t θ = \frac{b}{p} = \frac{6}{3} = 2 c s c θ = \frac{h}{p} = \frac{3 \sqrt{5}}{3} = \sqrt{5} s e c θ = \frac{h}{b} = \frac{3 \sqrt{5}}{6} = \frac{\sqrt{5}}{2}$

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Determine the hypotenuse

Step 3. Determine the trigonometric ratios.

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Determine the hypotenuse

Step 3. Determine the trigonometric ratios.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Applied Mathematics

Geometry

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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