Inverse COT, SEC, and CSC │Please Help!

Question

Round to the nearest degree. Show your work.

1. Cot (k) = 0.8765 ; k = ?
2. Sec(θ) = 1.6521; θ = ?
3. csc(a) = 1.3092; a = ?

Answer 1

Round to the nearest degree. Show your work.

1. Cot (k) = 0.8765 ; k = ?
2. Sec(θ) = 1.6521; θ = ?
3. csc(a) = 1.3092; a = ?

First of all, you cannot use cot, sec, csc on the calculator. Because, it has only sin, cos, and tan.

So, we converted them into sin,cos, and tan

cot(k) = 0.8765 => 1/tan(k) = .8765 => we take reciprocal both sides: tan(k) = 1/.8765 ~~1.14090

sec(theta) = 1.6521 => 1/cos(theta) = 1/1.6521=> cos(theta)~~.60529

csc(a) = 1.3092 => 1/sin(a) = 1/1.3092 => sin(a) ~~ .763825

Now we use calculator (arcsin, arccos, arctan & check you are using 'DEG', No RAD)

k=arctan(1.14090) = 48.765 ~~ 49 deg

theta = arccos(.60529) = 52.75028706 ~~ 53 deg

a = arcsin(.763825) = 49.80257179 ~~~ 50 deg

Answer 2

cot(k) = 1/tan(k),

So tan(k) = 1 / 0.8765

Take the inverse tangent of both sides and

k ≈ 48.7654349426 or rounded to the nearest degree, 49 degrees.

sec(x) = 1/cos(x)

So cos(x) = 1 / 1.6521

Take the inverse cosine of both sides and

x (or theta) ≈ 52.7502700214 or rounded to the nearest degree, 53 degrees.

csc(a) = 1/sin(a)

So sin(a) = 1 / 1.3092

Take rhe inverse sine of both sides and

a ≈ 49.8025928092 or rounded to the nearest degree, 50 degrees.