Question

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the exact value of the expression. 1) tan-1 (-1) 1) 2) 2) sin-1 (-0.5) show calculation 3) 3) cos-1 please Use a calculator to find the value of the expression rounded to two decimal places. 4) tan-1 (0.8) 4) U Find the exact value of the expression. Do not use a calculator. 39 5) 5) cos-1 6) Find the inverse function f-1 of the function f. 6) f(x) - 5 cos x + 8 Find the exact value of the expression. 7) castan 7) 8) col sin Use a calculator to find the value of the expression in radian measure rounded to two decimal places. 9) see-1 sect(

show calculations please.

Answer 1

0 tan" (-1) from the property, tan'(-x) = -tan'(x) So, tan'tu) = tan (1) T 4 As, We know, tani (1) = I 4 tan't) -TT Sin''(-0.5) can also be written as, sin'(- / ) so, by Property, sin" (-2) = -sin' () let Sin' (0.5) = - Flo 3 Cos'(-5) cost (-3 180°- Cos'(3) 180°– 30° 150 5T Cos'13= 56 e Given to Use a Calculator, for tan (0.8), Given, tan''(0.8) 0.6747 = 38.66 tan' (0.8) = 38.66 (rounded to two decimal ) CS Scanned with CamScanner

© Cos' (Cos (-5)) By the Property, cos(-x) = cos(x) C05'Cos (1) - Cos'( cos(35)) 310 Cos(cos(-35)) - 5 108 5 = f(x) 5 cos X + 8 + 9 = 5 Cosx+ + for the Inverse function, Interchange the Variables x and y, SO y = 5 COS X + 8 x=5 Cosy + 8 5 cosy X-8 X-8 5 cosy y = cos' (85) {"(x) = cos' (**) cos (ton' (-10) By the trigonometvic Property, tan'(-x)= - tan'(x) Cos (tan'(')) = Cos (-tan'l's)) By the trigonometric Idenity, Cos (tan"(x)) (By Property, cos ftan"(')) costar'(3)) J109 JI+('3)2 Cos'tan'(19)) 1109 Cosltan''s) = hor Jitxa 1 + x2 cos (-x) = cos(x) 3 X 109 1 + 100 9 CS Scanned with CamScanner

Cot (sin"(-3)) By Property, sin "(-x) = -538'(x) .. Cot ( strº"(+})) - Cot (- sin"(*)) Now, By Property, Cot (-x) = - cotx, cot (sir' (3) 5. Cot (- sti'() - By Identity (trigonometric), Cot (sin(x)) = VI- I-X² Х Ji-) Now, -Cot (Sini) UN - 2 niu - Cot (sin" (- 2 - )) ald @ Given, By using Calculator, (value of expression in radrans) Seell) Sec'(-5) = 2.18 (rounded to two dhe mal places) 2.1790 CS Scanned with CamScanner