Question

IF 0 ≤theta°≤360°find cos(2theta-10°)=-1/2

Answer 1

Answer:

θ

can be in the first quadrant

0

≤

θ

≤

90

or the fourth quadrant

270

≤

θ

≤

360

If

θ

is in the first quadrant,

then

sin

θ

=

5

13

cos

θ

=

12

13

tan

θ

=

5

12

Therefore,

sin

2

θ

=

2

sin

θ

cos

θ

=

2

×

5

13

×

12

13

=

120

169

cos

2

θ

=

cos

2

θ

−

sin

2

θ

=

(

12

13

)

2

−

(

5

13

)

2

=

144

169

−

25

169

=

119

169

If

θ

is in the fourth quadrant,

then

sin

θ

=

−

5

13

cos

θ

=

12

13

tan

θ

=

−

5

12

Therefore,

sin

2

θ

=

2

sin

θ

cos

θ

=

2

×

−

5

13

×

12

13

=

−

120

169

cos

2

θ

=

cos

2

θ

−

sin

2

θ

=

(

12

13

)

2

−

(

−

5

13

)

2

=

144

169

−

25

169

=

119

169