All categories

2 years ago

Find the exact value of the indicated trigonometric function of θ.

Mathematics

1 answer:

Mariana [72]2 years ago

8 0

Answer:

cosθ = -√(35/36)

tanθ = -1/√35

Step-by-step explanation:

We know that

sin²θ + cos²θ = 1

(1/6)² + cos²θ = 1

1 - (1/6)² = cos²θ

35/36 = cos²θ

sec θ = 1/ cosθ

1/ secθ = cos θ

Because secθ < 0, 1/ secθ would also be < 0, so cos θ < 0

cosθ = -√(35/36)

tanθ = sinθ/cosθ = (1/6)/-√(35/36)

= (1/6) / -(√35/6)

= -1/√35

You might be interested in

Find dy/dx given that y = sin x / 1 + cos x

kobusy [5.1K]

Answer:

$\frac{1}{1 + \cos(x) }$

Step-by-step explanation:

$y = \frac{ \sin(x) }{1 + \cos(x) }$

<u>differentiating numerator wrt x :-</u>

(sinx)' = cos x

<u>differentiating denominator wrt x :- </u>

(1 + cos x)' = (cosx)' = - sinx

Let's say the denominator was "v" and the numerator was "u"

$(\frac{u}{v} )' = \frac{v. \: (u)' - u.(v)' }{ {v}^{2} }$

here,

since u is the numerator u= sinx and u = cos x
v(denominator) = 1 + cos x; v' = - sinx

$= \frac{((1 + \cos \: x) \cos \: x )- (\sin \: x. ( - \sin \: x) ) }{( {1 + \cos(x)) }^{2} }$

$= \frac{ \cos(x) + \cos {}^{2} (x) + \sin {}^{2} (x) }{(1 + \cos \: x) {}^{2} }$

since cos²x + sin²x = 1

$= \frac{ \cos \: x + 1}{(1 + \cos \: x) {}^{2} }$

diving numerator and denominator by 1 + cos x

$= \frac{1}{1 + \cos(x) }$

6 0

3 years ago

Mrs. Wilbur can grade a set of 30 test in 2 hours. What is Miss wilbur rate per hour?

otez555 [7]

Answer: 15 tests per hour.

Step-by-step explanation: Mrs. Wilbur did 30 tests in 2 hours, so you would divide to find the rate per hour. 15 should be your answer.

5 0

2 years ago

Read 2 more answers

How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is not allowed?

shepuryov [24]

answer

c) 2520

Step-by-step explanation:

1st digit 1 of 7

2nd digit 1 of 6

3rd digit 1 of 5

4th digit 1 of 4

5th digit 1 of 3

7*6*5*4*3=2520 combination

8 0

2 years ago

Need help with number 20

olga2289 [7]

4^4x = 8
since 4 = 2^2 & 8= 2^3
so we can write the equation as
(2^2)^4x = 2^3
2^8x =2^3
sp ,, 8x = 3
then x = 3/8

5 0

2 years ago

-43 - 4r = 3(1 - 9r)

kap26 [50]

Answer

r = 2

Step-by-step explanation:

6 0

2 years ago