# Sec(x) = -1.5 trig help?

Sec(x) = -1.5, pi/2 and pi

find the remaining trig ratios, sin, cos, tan, cot, csc

Relevance
• Lucy
Lv 7

Given: sec x = -1.5 = -3 / 2

Remember sec x = 1 / cos x = 1 / (adjacent / hypotenuse) = (hypotenuse / adjacent).

Draw a diagram.

.......|\...../|\

.....x|..\..3|

.......|....\..|

<-----|------\|------------->

.........-2...|

...............|

..............\|/

Remember the Pythagorean Theorem.

a² + b² = c² (where a and b are legs and c is the hypotenuse)

Apply the formula.

a² + b² = c²

(-2)² + x² = 3²

4 + x² = 9

x² = 9 - 4

x² = 5

√(x²) = ± √5

x = ± √5

From the diagram, x is positive.

x = √5 = opposite

Remember that sin = opposite / hypotenuse.

sin x = (√5 / 3)

Remember that cos x = 1 / sec x.

cos x = 1 / (-3 / 2) = (-2 / 3)

Remember that tan = sin / cos.

tan x = (√5 / 3) / (-2 / 3) = (-√5 / 2)

Remember that cot = 1 / tan.

cot x = 1 / (-√5 / 2) = (-2 / √5) = (-2 / √5)(√5 / √5) = (-2√5 / 5)

Remember that csc = 1 / sin.

csc x = 1 / (√5 / 3) = (3 / √5) = (3 / √5)(√5 / √5) = (3√5 / 5)

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