Question

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Answer 1

Answer:

$\displaystyle x = \frac{3}{4}$

Step-by-step explanation:

we are given that

$\displaystyle P = \left(x, - \frac{ \sqrt{7} }{4} \right)$

we want to figure out x

remember that,

In unit circle x coordinate is considered cos and y coordinate is considered sin

so in order to figure out x we should figure out the value of cos to do we can consider Pythagoras trig indentity

given by

$\displaystyle \sin ^{2} ( \theta) + { \cos}^{2} ( \theta) = 1$

we are given sin=-√7/4 thus

substitute:

$\displaystyle \left( - \frac{ \sqrt{7} }{4} \right) ^{2} + { \cos}^{2} ( \theta) = 1$

simplify square:

$\displaystyle \frac{7}{16} + \cos ^{2} ( \theta) = 1$

move left hand side expression to right hand side and change its sign:

$\displaystyle \cos ^{2} ( \theta) = 1 - \frac{7}{16}$

simplify Substraction:

$\displaystyle \cos ^{2} ( \theta) = \frac{9}{16}$

square root both sides:

$\displaystyle \cos ^{} ( \theta) = \pm\frac{3}{4}$

since in unit circle cos is x and P belongs to Q:IV negative cos isn't applicable

hence,

$\displaystyle x = \frac{3}{4}$