# What does #-csc(arc cot(7))+2csc(arctan(5))# equal?

##### 2 Answers

-5.03

#### Explanation:

S = -csc(arccot (7)) + 2csc(arctan (5))

Use calculator -->

a. cot x = 7 --> tan x = 1/7

arccot(7) = arctan(1/7) --> arc

sin x = sin 8^@13 = 0.14 -->

b. tan y = 5 --> arc

sin y = sin 78^@69 = 0.98

Finally,

S = - 707 + 2(1.02) = -5.03

#### Explanation:

This is solvable without a calculator. It all depends on drawing pictures of the triangles.

For

Since cotangent is equal to the adjacent side of the angle in question divided by the opposite side, we can say that

Through the Pythagorean Theorem,

Since we want to find cosecant of this triangle, we will take the hypotenuse over the opposite side, so

#csc("arccot"(7))=sqrt50/1#

and

#-csc("arccot"(7))=-sqrt50#

We can find

If the tangent of an angle is

We want to find the cosecant of this angle as well, which will be

Thus

#csc(arctan(5))=sqrt26/5#

and

#2csc(arctan(5))=(2sqrt26)/5#

So, combining these, we see that

#-csc("arccot"(7))+2csc(arctan(5))=-sqrt50+(2sqrt26)/5#