SOLUTION: Indicate whether each of the following is true or false. sin 25° = sin 155° tan 20° = cot 70° sinƟ = cos(90-Ɵ) tanƟ = -cot(90-Ɵ) sinƟ = 1/cscƟ, w

Algebra ->  Trigonometry-basics -> SOLUTION: Indicate whether each of the following is true or false. sin 25° = sin 155° tan 20° = cot 70° sinƟ = cos(90-Ɵ) tanƟ = -cot(90-Ɵ) sinƟ = 1/cscƟ, w      Log On


   

Question 551241: Indicate whether each of the following is true or false.
sin 25° = sin 155°
tan 20° = cot 70°
sinƟ = cos(90-Ɵ)
tanƟ = -cot(90-Ɵ)
sinƟ = 1/cscƟ, where sinƟ is not 0
cosƟ = 1/secƟ, where cosƟ is not 0
sinƟ is never greater than 1 or less than -1
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
sin 25° = sin155°
155° is in the 2nd quadrant, and has a reference angle of 180°-155° = 25°
and the sine is positive in both the 1st and 2nd quadrants.  So the answer is
yes

tan 20° = cot 70°
Yes because 
1. cotangent and tangent are cofunctions of each other, 
2. Co-functions of complementary angles are equal.
3. 20° and 70° are complementary because their sum is 90°

sinƟ = cos(90-Ɵ)
Yes, because
1. cosine and sine are cofunctions of each other, 
2. Co-functions of complementary angles are equal.
3. Ɵ° and 90°-Ɵ are complementary because their sum is 90°

tanƟ = -cot(90-Ɵ)
No, because
1. cotangent and tangent are cofunctions of each other, 
2. Ɵ° and 90°-Ɵ are complementary because their sum is 90°
3. Co-functions of complementary angles are equal, so one 
cannot have the opposite sign from the other!

sinƟ = 1/cscƟ, where sinƟ is not 0
Yes, because sine and cosecant are reciprocal trig functions.

cosƟ = 1/secƟ, where cosƟ is not 0
Yes, because cosine and secant are reciprocal trig functions.

sinƟ is never greater than 1 or less than -1
True because the sine is opposite%2Fhypotenuse and the opposite is
never greater than the hypotenuse.

Edwin