Question

name all angles in the interval 0°≤θ<360° that make each statement true. sinθ = cos 130°

Answer 1

cos(130) is negative so the answer will be where the sin is negative which is the 3rd and 4th quadrant, if you type in a calc sin^-1(cos(130)) I get for one answer -40 or in other words 320 degrees

Answer 2

The other answer will be in the 3rd quadrant with the same reference angle.

Answer 3

Thank you, btw if secθ = csc 123° , i cant type it in the calculator so i dont know what to do?

Answer 4

well csc equals 1/sin

Answer 5

then do you know how i can type that in the calculator?

Answer 6

sure either sin and then the 1/x button or 1/sin(123) or sin(123) and then take to the -1 power.

Answer 7

alternatively the csc of 123 like the sin of 123 is positive, so find the reference angle for 123 you will want answers with the reference angle of 90-reference angle in the 1st and 4th quadrant.

Answer 8

thank you

Answer 9

\[\sin \theta=\cos 130=\cos \left( 90+40 \right)=-\sin 40\]
\[\sin \theta=-\sin 40=\sin (180+40),\sin (360-40)=\sin 220,\sin 320\]
\[\theta=220,320\]