#10 1. Write the following expressions in terms of only sin(0) and cos(0). Simplify sthat no quotients are in the expression7. Find the exact value of each real number y in radians.cot(0)(a) y = sin-'(Y2)(a) sec²(0) – tan²(0)(c)sec(0)(b) y = arccos(-)(b) tan2(0)(1+cot² (0))(c) y = sec-'(-2)%3D|2. Use the trigonometric identities to find the values of the functions below give:that cos(x) = and 0 is in quadrant IV(a) sin(x)(c) cot(-x)(d) y = arccot(-1)(b) tan(x)8. Evaluate each expression without using a calculator.(a) sin(arccos()3. Find sin(x+y), cos(x-y) and tan(x+y) using the following values(a) sin(x) = -, cos(x) = - and x and y in quadrant 3(b) cos(arctan(3))25(c) arcsec(sec(7))(b) sin(y) = -, cos(x) = - with x in quadrant 2 and y in quadrant 3%3D4. Find the values of sine and cosine given the following angles.(a) cos(20) = - and 0 in quadrant 19. Solve each equation for exact solutions between 0 and 27(a) sin²(x) = 1(b) cos(2B) = and 540° < 2B < 720°5. Use half angle identities to find each of the following:(b) 2 tan(x)-1=0(a) Find cos(;) if cos(0) =- with 0 in quadrant 2(b) Find sin() if cos(A)- with 90° < A< 180°10. Solve each equation for exact solutions between 0 and 360 degrees6. Match each of the following trigonometric expressions with an expression below:(a) sin2(0) + 3sin(0) + 2 = 0(a) sin?x – sin?y =Matching Bank:sec?x2 – 2cos (x)|sin(2x)(Ь)sin(x)cos²(y) – cos?(æ)(b) 2tan2(0) = tan(0) +12sec(r)(c) tan(x)sin(2x) =(d)2tan(x)sin(2x)(c) sin(0) – cos(20) = 0-

Name: #10 1. Write the following expressions in terms of only sin(0) and cos
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Description: #10 1. Write the following expressions in terms of only sin(0) and cos(0). Simplify sthat no quotients are in the expression7. Find the exact value of each real number y in radians.cot(0)(a) y = sin-'(Y2)(a) sec²(0) – tan²(0)(c)sec(0)(b) y = arccos(-

Answered: 10. Solve each equation for exact…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.3: Trigonometric Functions Of Real Numbers

Problem 44E

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#10

1. Write the following expressions in terms of only sin(0) and cos(0). Simplify s
that no quotients are in the expression
7. Find the exact value of each real number y in radians.
cot(0)
(a) y = sin-'(Y2)
(a) sec²(0) – tan²(0)
(c)
sec(0)
(b) y = arccos(-)
(b) tan2(0)(1+cot² (0))
(c) y = sec-'(-2)
%3D
|
2. Use the trigonometric identities to find the values of the functions below give:
that cos(x) = and 0 is in quadrant IV
(a) sin(x)
(c) cot(-x)
(d) y = arccot(-1)
(b) tan(x)
8. Evaluate each expression without using a calculator.
(a) sin(arccos()
3. Find sin(x+y), cos(x-y) and tan(x+y) using the following values
(a) sin(x) = -, cos(x) = - and x and y in quadrant 3
(b) cos(arctan(3))
25
(c) arcsec(sec(7))
(b) sin(y) = -, cos(x) = - with x in quadrant 2 and y in quadrant 3
%3D
4. Find the values of sine and cosine given the following angles.
(a) cos(20) = - and 0 in quadrant 1
9. Solve each equation for exact solutions between 0 and 27
(a) sin²(x) = 1
(b) cos(2B) = and 540° < 2B < 720°
5. Use half angle identities to find each of the following:
(b) 2 tan(x)-1=0
(a) Find cos(;) if cos(0) =
- with 0 in quadrant 2
(b) Find sin() if cos(A)
- with 90° < A< 180°
10. Solve each equation for exact solutions between 0 and 360 degrees
6. Match each of the following trigonometric expressions with an expression below:
(a) sin2(0) + 3sin(0) + 2 = 0
(a) sin?x – sin?y =
Matching Bank:
sec?x
2 – 2cos (x)
|
sin(2x)
(Ь)
sin(x)
cos²(y) – cos?(æ)
(b) 2tan2(0) = tan(0) +1
2
sec(r)
(c) tan(x)sin(2x) =
(d)
2tan(x)
sin(2x)
(c) sin(0) – cos(20) = 0
-

Expert Solution

Step 1

(10)(a)

$\begin{matrix} \sin^{2} θ + 3 \sin θ + 2 = 0 \\ \sin^{2} θ + 2 \sin θ + \sin θ + 2 = 0 \\ \sin θ (\sin θ + 2) + (\sin θ + 2) = 0 \\ (\sin θ + 1) (\sin θ + 2) = 0 \\ \sin θ + 1 = 0 a n d \sin θ + 2 = 0 \\ \sin θ = - 1 a n d \sin θ = - 2 \end{matrix}$

Use the graphical method, to determine the values for $θ$ in the $[0, 2 π]$ .

From graph, $θ = \frac{3 π}{2}$ .

Step 2

(b)

$\begin{matrix} 2 \tan^{2} θ = \tan θ + 1 \\ 2 \tan^{2} θ - \tan θ - 1 = 0 \\ 2 \tan^{2} θ - 2 \tan θ + \tan θ - 1 = 0 \\ 2 \tan θ (\tan θ - 1) + (\tan θ - 1) = 0 \\ (2 \tan θ + 1) (\tan θ - 1) = 0 \\ 2 \tan θ + 1 = 0 a n d \tan θ - 1 = 0 \\ 2 \tan θ = - 1 a n d \tan θ = 1 \\ \tan θ = - \frac{1}{2} a n d \tan θ = 1 \end{matrix}$

Again, use the graphical method, to determine the values for $θ$ in the $[0, 2 π]$ .

From the graph $θ = 45 °, 153 .44 °, 225 °, 333 .44 °$ .

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