If 0 degree lessthanorequalto theta lessthanorequalto 360 de

If 0 degree lessthanorequalto theta lessthanorequalto 360 degree, find the value of theta that makes each statement true. Express your answer in degrees. Remember, there may be more than one answer!! sec theta = - Squareroot 2 cos theta = 0 and tan theta is undefined Sin theta = - Squareroot 3/2 and cos theta greaterthanorequalto 0

Solution

a) sec(theta)=-sqrt(2)

when sec(135⁰),sec(225⁰),then  sec(theta)=-sqrt(2)

therefore theta =135⁰,225⁰

b) cos (theta)=0 and tan (theta) is undefined

when cos (90⁰),cos (270⁰) then cos(theta)=0 and when tan(90⁰),tan(270⁰)=tan(theta) is undefined

therefore theta =90⁰,270⁰

c)sin (theta) = -(sqrt(3))/2 and cos(theta) (greater than or equal)0

when sin (300⁰) =-(sqrt(3))/2 and cos(300⁰)=1/2 which is (greater than or equal)0

therefore theta=300⁰