Question

1. What is the value of x?

sin(x+22)°=cos(2x−7)°

2.Given cosx=1213 and sinx=513

.

What is ratio for ​ tanx

​ ?

leave answer as a fraction in simplest form

Answer 1

Part 1)
sin(x+22)°=cos(2x−7)°

we know that
the sine and cosine are co-functionsSosin (theta) = cos (90 - theta)------> This implies that the angles sum to 90°therefore( x + 22) + (2x - 7) = 90 simplify3x + 15 = 90 subtract 15 from both sides3x = 75 divide both sides by 3x = 25 The answer Part 1) is x=25° Part 2) Given cos x=12/13 and sin x =5/13What is ratio for ​ tanx ​ ? we know thattan x = sinx / cos xtan x = (5/13) / (12/13) = (5/13) * (13/12) = 5/12the answer Part 2) is 5/12