Choose all answers that are correct.

Step-by-step explanation:

In quadrant IV, the tangent is negative, so the first answer choice cannot be correct.

The triangle involved is a 3-4-5 triangle, so the second answer choice cannot be correct.

The cosecant can be found several ways. One is to find the sine of the angle (-4/5 — compare to answer choice 2), then invert it. (csc(θ) = 1/sin(θ)) Here that means csc(θ) = 1/(-4/5) = -5/4, in agreement with the third answer choice.

cos(θ) = 1/sec(θ) = 1/(5/3) = 3/5, in agreement with the fourth answer choice.

Comment on cosecant

You know from SOH CAH TOA that ...

  Cos = Adjacent/Hypotenuse

Then Sec = 1/Cos = Hypotenuse/Adjacent. This can help you draw the triangle, which you quickly realize is a 3-4-5 right triangle. If not, you can use the Pythagorean theorem to find the opposite side length as ...

  √(5²-3²) = √16 = 4

Remember the triangle is being drawn in the 4th quadrant, so the side opposite the angle will be negative.

Of course, Csc = 1/Sin = Hypotenuse/Opposite, so is 5/(-4) = -5/4.

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841