Given that cosine of theta = (-sqrt6/4), pi/2 <0< pi, find the exact value of each of the following:?

Question

(a) sin(2theta) (b) cos(2theta) (c) sin(theta/2) (d) cos(theta/2)

 

Answer 1

(a)

The given value .

Step 1 :

From cosine function

Hypotenuse = 4

Adjacent = - √6

From Pythagorean theorem

Formula for sine function :

Step 2 :

To find value of sin 2θ

Apply double angle of sine function formula :

Solution :

Answer 2

(b)

The given value .

Step 1 :

From cosine function

Hypotenuse = 4

Adjacent = - √6

From Pythagorean theorem

Formula for sine function :

Step 2 :

To find value of cos 2θ

Apply double angle of cos function formula :

Substitute and   in above formula

Solution :

Answer 3

(c)

The given value .

Step 1 :

From cosine function

Hypotenuse = 4

Adjacent = - √6

From Pythagorean theorem

Formula for sine function :

Step 2 :

To find value of sin(θ/2)

Apply half angle of sine function formula :

Substitute   in above formula

Rewrite the expression with common denominator.

Solution :

Answer 4

(d)

The given value .

Step 1 :

From cosine function

Hypotenuse = 4

Adjacent = - √6

From Pythagorean theorem

Formula for sine function :

Step 2 :

To find value of cos(θ/2)

Apply half angle of sine function formula :

Substitute   in above formula

Rewrite the expression with common denominator.

Solution :