Question

Find a value of theta for which the statement is true.

Theta will represent x here.

tan x = cot5x

Answer 1

the above equation can become cot5x * cotx = 1 or cos5x*cosx - sin5x * sinx =0

Does this help ?

Answer 2

Idk all i did was x plus 5x equals 90

Answer 3

got x equals 15 dont know hat to do next

Answer 4

Is this: cot5x

cot^5 x or is it cotangent of (5*x) ?

Answer 5

ill show you on my paper

Answer 6

Okay

Answer 7

not just 90 but \[\pm90+360k\] where k is any integer

Answer 8

or in pi notation:
\[\pm \frac{ \pi }{ 2 } + 2\pi k\]

Answer 9

Its number 18

Answer 10

if it is just one value then \[\pi /12\] or 15 degrees is fine

Answer 11

Thanks for posting that. @SuperFly123

Answer 12

xavier i dont understand what your doing sorry

Answer 13

No prob @Directrix

Answer 14

@SuperFly123 - i thought you needed a generalised solution not just one angle :)

Anyhow, for one acute angle your answer should be correct

Answer 15

I think you can use an addition formula to simplify the problem.
first change things in sin and cos

Answer 16

But i think i need to find the exact value

Answer 17

phi, how?

Answer 18

@SuperFly123 Where in the first quadrant is tan(θ) = 1 ?

Answer 19

write tan and cot in terms of sin and cos. do you know how to do that ?

Answer 20

@SuperFly123 - Can you show your approach ?

Answer 21

no phi, and ill show you how my teacher did an example

Answer 22

ok, do that, because there are probably a few different ways to tackle this.

Answer 23

tan x= cot 5x= tan (90°-5x)
So x=90-5x
6x=90
x=15°
,,

Answer 24

yes, that's pretty.

Answer 25

\[ \frac{\sin x}{\cos x}= \frac{\cos 5x }{\sin 5x} \\ \sin x \sin 5x = \cos 5x \cos x \\
\cos 5x \cos x - \sin5x \sin x =0\\
\cos(6x)= 0\]

Answer 26

I think , it can have more than one solutions.

Answer 27

>>Find a value of theta

The question sounds as if one value will suffice.

Answer 28

yes, my approach might be overkill

Answer 29

Sure

Answer 30

I got 15 what do i do from there

Answer 31

How about a basic approach of knowing that tan 45 = 1 and

knowing that 5*45 = 225 degrees, the cotangent of which is 1.

That gives π/4 as an angle that satisfies the equation.

Answer 32

But, where do we get 45 from

Answer 33

From the basic trig values I had to learn.

Answer 34

The table comes from right triangle trig.

Answer 35

Since, my teacher didnt get up to that yet i dont think i should use that approach

Answer 36

Okay.

Answer 37

I dont know what to do omg

Answer 38

What i have so far is tan 15 = cot 75
Then tan 15 = 1/tan(45+30) giving me a right answer

Answer 39

you should fix question 4.

The "trick" is if you are told a function and it's "cofunction" are equal
then the sum of the two angles is 90 degrees

for example, if you are told
sin (A) = cos(B)
then A+B= 90

or if
tan A = cot B
then A+B= 90

Answer 40

Yeh i know i got that wrong

Answer 41

so in question 4, you don't set the two expressions equal to each other.
you add them up, and set that sum equal to 90

Answer 42

for the
tan x = cot (5x)
you do
x+5x= 90
6x= 90
x= 15
which gives one (of multiple possible) answers

Answer 43

yeh so the answer is just 15

Answer 44

yes :)

Answer 45

Alright then

Answer 46

can you do these problems?

for example 13: sin 10 = cos x
they are "co functions" so you can write
10+x= 90
x= 80
(using a calculator we can check sin 10 = cos 80)