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Chapter 9: Q. 5 (page 582)

$\sin \frac{5 π}{4} =________.$

Short Answer

Expert verified

The value of $\sin \frac{5 π}{4} = - \frac{1}{\sqrt{2}} .$

Step by step solution

01

Step 1. Given Information

The sine function is a periodic function. The ratio of the perpendicular and the hypotenuse is called the sine function.

02

Step 2. Filling the blank

We can write $\sin \frac{5 π}{4}$ as $\sin (π + \frac{π}{4}) .$

As we know sine function is negative in the third quadrant.

Thus,

$\sin (\frac{5 π}{4}) = \sin (π + \frac{π}{4}) \sin (\frac{5 π}{4}) = - \sin (\frac{π}{4}) \sin (\frac{5 π}{4}) = - \frac{1}{\sqrt{2}}$

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Most popular questions from this chapter

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

$(- 2, 0)$

In Problems 11–22, plot each complex number in the complex plane and write it in polar form. Express the argument in degrees.

$3 - 4 i$ .

Find each quantity if $v = 3 i - 5 j$ and $w = - 2 i + 3 j$ .

$3 v - 2 w$

Identify and graph each polar equation. Verify your graph using a graphing utility

$r = 3 - 3 \sin θ$

Use the figure at the right. Determine whether the given statement is true or false.

$E + D = G + H$

See all solutions

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