1. Simplify and write the trigonometric expreission in terms of sine and cosine:
ID: 2833575 • Letter: 1
Question
1. Simplify and write the trigonometric expreission in terms of sine and cosine:
(1-cos(y)) (1+cos(y)) = (f(y))^2 f(y) = ____
2. Simplify and write the trig expression in terms of sin and cosine.
sec t - cos t / sec t = (f(t))^2 f(t) = ____
3.The expressions A,B,C,D, E are left hand sides
of identities. The expressions 1,2,3,4,5 are right hand side of
identities. Match each of the left hand sides below with the appropriate
right hand side. Enter the appropriate letter (A,B,C,D,
or E) in each blank.
A. tan(x)
B. cos(x)
C. sec(x) csc(x)
D. 1-(cos(x)^)2 /cos(x)
E. 2sec(x)
1. sec(x)-sec(x)(sin(x))^2 ___
2. sin(x) tan(x) ___
3. cos(x) / 1-sin(x) + 1-sin(x) / cos(x) ____
4. sin(x) sec(x) ____
5. tan(x)+cot(x) ____
4.For each trigonometric expression A,B,C,D, E,
choose the expression from 1,2,3,4,5 that completes a fundamental
identity. Enter the appropriate letter (A,B,C,D, or E) in
each blank.
A. (sin x)^2+(cos x)^2
B. sin x / cosx
C. (tan x)^2+1
D. cosx /sin(x)
E. (sin x)^2
1. tan x ____
2. (sec x)^2 ___
3. cot x ____
4. 1 ____
5. 1-(cos x)^2____
5.
Let f (x) =12tan x+7 / sec x
f ' (x) = ____
f ' ( -pie / 4 ) = ____
6.Find the equation of the tangent line to the curve
y=6tan x at the point (pie/4;6). The equation of this tangent line
can be written in the form y = mx+b where m is:______
and where b is:______
7.Let
f (x) = 9xsinxcosx
f ' (3pie/ 2 ) = _____
8.Find the equation of the tangent line to the curve y = 3x cos x
at the point (pie;-3pie).
The equation of this tangent line can be written in the form
y = mx+b where
m = ______ and b =_____-
9.Match the functions and their derivatives:
1. y = cos(tan(x)) _____
2. y = sin(x) tan(x) ____
3. y = cos^3(x) ____
4. y = tan(x) _____
A. y0 = -3cos^3(x) tan(x)
B. y0 = -sin(tan(x))/cos^2(x)
C. y0 = 1+tan^2(x)
D. y0 = sin(x)+tan(x) sec(x)
Explanation / Answer
1) siny
2) sint
3)
A --> 4
B --> 1
C --> 5
D--> 2
E -->3
4)
A --> 4
B --> 1
C --> 2
D --> 3
E --> 5
5) Let f (x) =12tan x+7 / sec x = 12tanx + 7cosx
f ' (x) = 12sec^2x - 7sinx
f ' ( -pie / 4 ) = 12 sec^2(-pi/4) - 7sin(-pi/4) = 24 + 7/sqrt2
6) y=6tan x at the point (pie/4;6).
y' = 6sec^2x
at pi/4, 6 , slope = y' = 6sec^2(pi/4) = 6*2 = 12
So equation of tangent is
y-6 = 12(x- pi/4)
=> y= 12x - 3pi +6
m= 12, c= -3pi+6
7.
f (x) = 9xsinxcosx
f'(x) = 9sinxcosx + 9xcos^2x - 9xsin^2x
f ' (3pie/ 2 ) = -27pi/2
8) y = 3x cos x
at the point (pie;-3pie).
y' = 3cosx - 3xsinx
at (pi, -3pi), slope = y' = 3cospi - 3pisinpi = -3
so, equation of tangent is
y-(-3pi) = -3*(x-pi)
=> y+3pi = -3x+3pi
=> y= -3x
m= -3, c=0
9)
1 --> B
2 --> D
3 --> A
4 --> C
PLEASE DO RATE> ASK IF ANY QUERY. I CAN EXPLAIN THE ANSWERS< IF YOU WANT :) HAPPY LEARNING !
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