+0

0
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+1982

Apr 17, 2020

#1
+498
+2

secant = 1/cos

Dividing by -sqrt3 on both sides

$$\sec{\theta} = -\frac2{\sqrt3}$$

Rationalizing the denominator by multiplying it by sqrt3/sqrt3(which is one):

$$\sec{\theta} = -2\sqrt{3}/3$$

Substituting in 1/cos:

$$1/\cos{\theta} = -2\sqrt{3}/3$$

$$\cos{\theta} = -3/2\sqrt{3}$$

Rationalizing like before by multiplying by sqrt3 / sqrt 3, we get:

$$\cos{\theta} = -3\sqrt{3}/6 = -\sqrt3/2$$

The values for which this is true between [0, 2pi] are :

$$\cos{5\pi/6}$$ radians (cos 150 degrees) and $$\cos{7\pi/6}$$(cos 210 degrees). The general forms for these are then indeed your answer because the period of cosine is 2pi.

Apr 17, 2020
#2
+1982
+1

thank you for your help! (: the explanation has helped

jjennylove  Apr 17, 2020