Question

Help on trig! Fan & medal

Answer 1

Find the exact value for tan(195 degrees)

Answer 2

is it 2-√3 ?

Answer 3

tan 195 can be written as

tan (180 + 15)

Rule:
tan (180 + 'anything') = tan ('anything')

So tan(180 + 15) = tan 15

Answer 4

Yes, i think it is. I have done this quite a number of times to be honest. O.O

Answer 5

No it has to be in radians

Answer 6

Oh okay how do i mke sure ?

Answer 7

Radians or degrees, the value will always be the same. :)

Is it tan (195 radians) ??? [Then it'd be different]

Answer 8

not its degrees but the answer has to be in radians

Answer 9

use the Unit Circle :)

Answer 10

yes 2-√3

Answer 11

Yes, it is \(2 - \sqrt{3}\)

The answer will be a ratio and will not be an angle [Like in radians or degrees]

Answer 12

keeping in mind that \(\bf tan(\theta)=\cfrac{y}{x}\)

Answer 13

Oh okay well thanks guys :)

Answer 14

:)

Answer 15

What about when it says for example find exact value for sin(π/3 - π/4) how do i do this :o

Answer 16

Do i just subtract and then find sin orrrr?

Answer 17

Do you know what

sin(A+B) expands to? :D

Answer 18

mmm no :/

Answer 19

To find the value in terms of irrational numbers, you need to know the property.

sin(A+B) = sinA.cosB + sinB.cosA :)

Answer 20

Hmm okay soo how would sin(π/3 - π/4) look like?

Answer 21

Take A = pi/3 , B = pi/4
And then try using the identity! ^^

pi/3 and pi/4 are in radians, convert them to angles in degrees to make the calculation much simpler. :)

Answer 22

Soooo.. (sin π/3* cos π/4 + sin π/4* cos π/3) ? :)

Answer 23

Yes! :D

Answer 24

awesome :) now i just put it in my calculator?

Answer 25

if it in radian = 0.224938
cause 1^r = 57.29578 degree

Answer 26

YES, you may use the calculator. :)
[We are not allowed to in our school]

Answer 27

it says find the exact value so doesnt that mean in radians tho? so can i use a calculator?

Answer 28

If you use a calculator you'll get decimal values which are pretty exact. :P

But if you do know the basic trigonometric equation values, you may use that.

pi/3 = 60
pi/4 = 45

So sin π/3 * cos π/4 + sin π/4 * cos π/3
= sin 60 * cos 45 + sin 45 * cos 60\[=\frac{\sqrt{3}* 1}{2* \sqrt{2}} + \frac{1* 1}{2* \sqrt{2}}\] \[= \frac{\sqrt{3} + 1}{2*\sqrt{2}}\]

sqrt{2} = 1.414
sqrt{3} = 1.732

now you can calculate with a calculator. :)

Answer 29

wait where did you get this 3√∗12∗2√+1∗12∗2√
haha?

Answer 30

Those are the basic trigonometric values. I remember them. :P
I am in grade 11, we sort of have to remember them, where I study. :D

Answer 31

Oh nvm i get it

Answer 32

Yes lol :p

Answer 33

yeah same im just bad at remembering those i have a table :p

Answer 34

They are not that difficult if you find a relation.

Like sin 30' = cos 60' = 1/2
and sin 60' = cos 30' = √3/2
and sin 45 = cos 45' = 1/√2

And so on and so forth. :D

Answer 35

Actually I do agree with you, it can be found out using a calculator, but sometimes it is better to remember the basic values. :)

Answer 36

Yeah haha :) so it would be 1.414 + 1/2 * 1.732 = 2.6?

Answer 37

It'll be

2.732/2.828

because √3 + 1 = 2.732
and 2*√2 = 2.828

Answer 38

0.96605 :)

Answer 39

Ohhh so you can round it up and the answer would be just 1 ?? :)

Answer 40

Yes, you may, but then I think they need the exact value. :)

Answer 41

oh yeah thats right :p my teacher told me that the exact value meant in radians sooo it would be 0.96605 radians?

Answer 42

No no no..

if x = sin y

then y is the angle and it may be in radians or degrees and x is just the value.

I can teach you a bit of trigonometry if you want. :)

Answer 43

Haha please :) i am so confused lol i have my final to take soon

Answer 44

Sure. So which grade are you in? And what are you learning in trigo now?

Answer 45

Im in 11th. Almost done with trig. I have an A and i've understood everything except a few things in the most recent lessons

Answer 46

Like identities

Answer 47

Like i dont get what verified trig identities are

Answer 48

Oh cool same as me. :D

Okay, so trigonometry is just ratios actually nothing tough with that.
The simplest way to understand that is by using a right angles triangle.



Here, a may be in radians or in degrees.

So sin(a) = some value.

a is in degrees or radians and 'some value' is just a ratio with no units absolutely. :)

Answer 49

Yeah that makes sense :)

Answer 50

Great.
You should try some yourself, and if you have a doubt just hit me up. :)

Answer 51

Okay thanks :)))) you are really a big help :) i'm going to do that problem over with subtraction. Do you mind checking it when im done?

Answer 52

Not at all. :)

Answer 53

Okay thanks :) so i dont use this formula anymore
sin(A+B)

Answer 54

No, but it is similar.

sin(A+B) = sinA.cosB + sinB.cosA
sin(A-B) = sinA.cosB - sinB.cosA
cos(A+B) = cosA.cosB - sinA.sinB
cos(A-B) = cosA.cosB + sinA.sinB

It may take some time, but it is helpful to remember these! ^

Answer 55

ok so we use sin(a - b)

Answer 56

tan(A+B) = \[\frac{tanA+tanB}{1-tanA.tanB}\]

tan(A-B) = \[\frac{tanA-tanB}{1+tanA.tanB}\]

Answer 57

Yes, and we do that, because it asks you in your question.

sin(pi/3 - pi/4)

Answer 58

wait why that one hahah that looks confusing :/

Answer 59

Oh okay good haha :p sooo

Answer 60

sin(A-B) = sinA*cosB + sinB*cosA
(sin pi/3* cos pi/4 - sin pi/4* cos pi/3)
sin 60 * cos 45 - sin 45 * cos 60
√3 * 1/2*√2 - 1 * 1/2*√2 =