Question

Consider this equation. cos(0)=-3/10 if 0 is an angle in quadrant ii, what is the value of tan(0)? sqrt91/10 -sqrt91/3 sqrt91/3 -sqrt91/10

Answer 1

The value of tan(x) is $-\frac{\sqrt{91}}{3}$ if cos(x) = -3/10 and the angle is in the second quadrant i.e. quadrant II

How to determine the value of tan(x)?

The expression is given as:

cos(x) = -3/10

Using the following trigonometry identity:

sin²(x) + cos²(x) = 1

The equation become

sin²(x) + (-3/10)² = 1

Evaluate the exponent

sin²(x) + 9/100 = 1

Subtract 9/100 from both sides

sin²(x)  = 91/100

Take the square root of both sides

$\sin(x) = \frac{\sqrt{91}}{10}$

Sine is positive in quadrant II.

So, the tangent is calculated using:

$\tan(x) = \sin(x) \div \cos(x)$

This gives

$\tan(x) = \frac{\sqrt{91}}{10} \div -\frac{3}{10}$

Evaluate

$\tan(x) = -\frac{\sqrt{91}}{3}$

Hence, the value of tan(x) is $-\frac{\sqrt{91}}{3}$

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