Question

For what value of x between -90^∘ and 90^∘ is tan 198^∘ = -tan x^∘?

a) x = 18^∘

b) x = -18^∘

c) x = 162^∘

d) x = -162^∘

Answer 1

The value of x for which tan(198°) equals -tan(x°) given the restrictions is -18°. This is because tan has a period of 180°, and the negative sign indicates it is in the fourth quadrant.

Step-by-step explanation:

To find the value of x for which tan(198°) = -tan(x°), we can use the properties of the tangent function and the periodicity of the trigonometric functions. Since tangent has a period of 180°, tan(198°) is equivalent to tan(18°), as 198° - 180° = 18°.

Moreover, the negative sign indicates that x must be in the quadrants where tangent is negative, which are the second and fourth quadrants.

However, the question specifies that x must be between -90° and 90°, meaning it must be in the fourth quadrant. Therefore, the equivalent negative angle for 18° in the fourth quadrant is -18°, which makes option (b) the correct answer.