Evaluate the expression under the given conditions.
sin(θ − ϕ); tan θ=12/5, θ in quadrent III, sin ϕ = -sqrt10/10, ϕ in quadrent IV

Question

Evaluate the expression under the given conditions.
sin(θ − ϕ); tan θ=12/5, θ in quadrent III, sin ϕ = -sqrt10/10, ϕ in quadrent IV

karisleft · Answer

|dw:1478126750725:dw|

karisleft · Answer

looks like that if it helps

shadowlegendx · Answer

@ParthKohli

parthkohli · Answer

yeah you just need to calculate $\cos \theta, \sin \theta, \cos \phi, \sin \phi$ but that shouldn't be troublesome because you're given all the data you need

parthkohli · Answer

the quadrants tell you the sign of the trigonometric ratios in a way, since a quadrant will uniquely determine the sign of your trig functions. 

and whenever you're given tan/cot, you can make a triangle to calculate the magnitudes of sine and cosine. 

i'd speak more on this, but tell me whether you've encountered this before

karisleft · Answer

this is the first, its a practice question in my book, trying to understand

parthkohli · Answer

If this is the first problem in your practice book, then you're using the wrong practice book.

karisleft · Answer

jeeez, well where do i start

satellite73 · Answer

use the subtraction angle formula $$\sin(A-B)=\sin(A)\cos(B)-\sin(B)\cos(A)$$

satellite73 · Answer

you got $\tan(\theta)=\frac{12}{5}$ from that you should be able to find $\cos(\theta)$ and $\sin(\theta)$