If sin x + cos x = 0 and x lies in the fourth quadrant, find sin x and cos x.

Asked by Aaryan | 1 year ago |  44

##### Solution :-

Given:

Sin x + cos x = 0 and x lies in fourth quadrant.

Sin x = -cos x

$$\dfrac{ Sin x}{cos x}$$ = -1

So, tan x = -1 (since, tan x = sin x/cos x)

We know that, in fourth quadrant, cos x and sec x are positive and all other ratios are negative.

By using the formulas,

Sec x = $$\sqrt{(1 + tan^2 x)}$$

Cos x =$$\dfrac{ 1}{sec x}$$

Sin x = $$- \sqrt{(1 -cos^2 x)}$$

Now,

Sec x = $$\sqrt{(1 + tan^2 x)}$$

= $$\sqrt{(1 + (-1)^2)}$$

$$\sqrt{2}$$

Cos x = $$\dfrac{ 1}{sec x}$$

$$\dfrac{1}{\sqrt{2}}$$

Sin x = $$– \sqrt{(1 – cos^2 x)}$$

$$\sqrt{-\dfrac{1}{2}}$$

$$- \dfrac{1}{\sqrt{2}}$$

sin x = $$- \dfrac{1}{\sqrt{2}}$$ and cos x = $$\dfrac{1}{\sqrt{2}}$$

Answered by Sakshi | 1 year ago

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