Simple Trig Questions, arg! (2 Viewers)

[Finx]

1. If sin x = 0.3, find:

i) cos(90-x)
ii) cos² x
iii) cosec x
iv) sin(180+x)
v) sin(360-x)

(You probably don't have to all of these, just explain what I'm supposed to do here =P)

2. What is the exact value of cos(-150°)?

5. If cos(theta)=0.96, find the exact value of cot(theta).

Thanks in advance! =]

 

[fishy89sg]

1. If sin x = 0.3, find:

i) cos(90-x)
ii) cos² x
iii) cosec x
iv) sin(180+x)
v) sin(360-x)

(You probably don't have to all of these, just explain what I'm supposed to do here =P)

2. What is the exact value of cos(-150°)?

5. If cos(theta)=0.96, find the exact value of cot(theta).

Thanks in advance! =]

1 i) cos(90-x) = sinx = 0.3
ii) cos² x = 1 - sin ² x = 1 - (0.3)(0.3) = 0.91
iii) cosecx = 1/sinx = 1/0.3 = 3.3333
iv) sin(180+x) = -sinx = -0.3
v) sin(360-x) = -sinx = -0.3

2. -sqrt3 /2
5. cos theta = 96/100
therefore constructing a right angled triangle, your third side is sqrt(100² - 96²) = 28
so tan theta = O/A = 28/96
cot theta = 96/28

 

[x.Exhaust.x]

With the 1st question, just manipulate them with your 3 trigonometric rules until you get sine. Then substitute the value in and if necessary, use ASTC to determine if it's positive or negative

Edit: Thumbs up for above post.

 

[kaz1]

1. If sin x = 0.3, find:

i) cos(90-x)
ii) cos² x
iii) cosec x
iv) sin(180+x)
v) sin(360-x)

(You probably don't have to all of these, just explain what I'm supposed to do here =P)

2. What is the exact value of cos(-150°)?

5. If cos(theta)=0.96, find the exact value of cot(theta).

Thanks in advance! =]

For 2. find the value cos(150) since the cos wave is an even function.

For 5 draw a triangle with 24 as the opposite side and 25 as the hypotenuse. Then find the third angle using Pythagoras and the rest is simple.

 

[Finx]

i) cos(90-x) = sinx = 0.3

^ What?

How'd you get that.

 

[kaz1]

^ What?

How'd you get that.

In a right angled triangle you have and angle theta and (90-theta).
Notice how cos (90-theta)=sin theta.

 

[Finx]

Notice how cos (90-theta)=sin theta.

No, I didn't notice this. We've probably done it in class and I wasn't paying attention. I'll look up a text book for it.

 

[fishy89sg]

No, I didn't notice this. We've probably done it in class and I wasn't paying attention. I'll look up a text book for it.

if you wanna know how its derived... you use the following 3unit formula:
cos(a-b) = cosacosb + sinasinb

so with a=90, b=theta:
cos(90 - theta) = cos90costheta + sin90sintheta = 0 + sintheta = sintheta

try it in your calculator... it sersly works

 

[Finx]

iv) sin(180+x) = -sinx = -0.3
v) sin(360-x) = -sinx = -0.3

I got v), but I don't get iv).

Is it possible to expand sin(180+x)?
Therefore giving sin180+sinx
= 0 + 0.3
= 0.3?

 

[lolman12567]

sin(180+x)

does the 180 + x show that the ray must lie in the 3rd quadrants where only tan is positive therefore making sin negative?

dunno, i'm quite confused about this topic myself

 

[Finx]

sin(180+x)

does the 180 + x show that the ray must lie in the 3rd quadrants where only tan is positive therefore making sin negative?

dunno, i'm quite confused about this topic myself

I think you're right.

 

[tommykins]

sin(180+x)

does the 180 + x show that the ray must lie in the 3rd quadrants where only tan is positive therefore making sin negative?

dunno, i'm quite confused about this topic myself

Yes

 

[lolokay]

I got v), but I don't get iv).

Is it possible to expand sin(180+x)?
Therefore giving sin180+sinx
= 0 + 0.3
= 0.3?

you can't expand a function that way
for sine, the expansion is:
sin(A+B) = sinAcosB + sinBcosA
so sin(180+x) = sin180cosx + cos180sinx
= -sin[x]

it's the negative of sin[x] because, by adding 180 you're flipping it - so the opposite side will have the same magnitude but be pointing downwards.
Similarly, cos(180+x) = -cos[x] because the adjacent has been flipped.
but tan(180+x) = tan[x] because both the opposite and adjacent have been flipped

sin[90-x] and similar identities can be found by observing the right-angled triangle, since the cosine at 1 angle is the same as the sine of the other.

 

[Finx]

you can't expand a function that way
for sine, the expansion is:
sin(A+B) = sinAcosB + sinBcosA
so sin(180+x) = sin180cosx + cos180sinx
= -sin[x]

You could've just said cos180 = -1.. lol =]

I understand that expansion, but isn't that 3 unit stuff? These questions were taken from a 2u paper.

 

[lolokay]

well, you asked about the sine expansion, and it says your doing 3u
you don't need that formula to figure out these questions, just think about it like I was saying - eg. the angle gets flipped either 180' or about the x or y axis, or they're complimentary angles, or whatever else, to figure out what it will be in terms of another angle

eg. sin(180-x),
180-x means that the angle will have been flipped about the y axis, but since the opposite side is still positive it will = sin[x]

 

[fishy89sg]

seriously guys, its soo much easier to sketch the graphs

when you sketch y=sin(180+x), the curve shifts 180 degrees to the left, so in effect, you get the curve y=-sinx

and y=sin(-x) = -sinx so sin(360-x) = -sin(360+x) and when thats sketched, its the same as -sinx since the sinx curve repeats itself every 360 degrees