If sec theta = and the reference angle of theta is 45∘, find both angles in degrees from 0∘ < theta < 360∘ and both angles in radians from 0 < theta < 2pi

Step-by-step explanation:

cos

θ

+

sin

θ

=

0

Since

cos

45

∘

=

sin

45

∘

,

cos

45

∘

cos

θ

+

sin

45

∘

sin

θ

=

0

cos

(

θ

−

45

∘

)

=

cos

90

∘

θ

−

45

∘

=

±

90

∘

+

360

∘

k

for integer

k

θ

=

45

±

90

∘

+

360

∘

k

θ

=

−

45

∘

+

180

∘

k

That's the same answer we got by knowing cotangent meant reciprocal slope, and we choose the one in the fourth quadrant as requested.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11