Trigonometric Functions

anpanman SG

Given that tan A = - 5 /12 and that tan A and cos A have opposite signs, find the value of cos A and of cos (pi/2 - A).

Can anyone tell me what the question means when it says,"opposite signs"?

Below is another question which I do not understand. Please take a look. (=

Given that sin 20 deg = k, express the following in terms of k.

i.tan(-20deg)

ii. sin 70 deg.

I think I just need help for part (i) of the question. I will attempt the second part on my own though.

Thanks for reading!

^tamago^ SG

Given that tan A = - 5 /12 and that tan A and cos A have opposite signs, find the value of cos A and of cos (pi/2 - A).

Can anyone tell me what the question means when it says,"opposite signs"?

tan A = sin A/cos A. If cos A and tan A can have opposite signs, it means there are solutions in all 4 quadrants since cos A can be positive or negative.

tan A = opp / adj = - 5 / 12.
hyp² = opp² + adj² = 5² + 12² = 13². ==> hyp = 13
cos A = adj / hyp = ± 12 / 13

cos (π/2 - A) = sin A = opp / hyp = ± 5 / 13

^tamago^ SG

Given that sin 20º = k, express the following in terms of k.

i. tan (-20º)

ii. sin 70º.

wishboy SG

Given that tan A = - 5 /12 and that tan A and cos A have opposite signs, find the value of cos A and of cos (pi/2 - A).

Can anyone tell me what the question means when it says,"opposite signs"?

opposite signs mean that if one is +ve, the other is -ve, and vice versa.

tan A = -5/12 (angle A falls in 2nd or 4th quadrant)

since they say tan A and cos A have opposite signs,
cos A is +ve (angle A falls in 1st or 4th quadrant)

so now u noe tat angle A is in the 4th quadrant

opp. = 5, adj. = 12, hyp. = 13

cos A = 12/13

cos (pi/2 - A)
= sin A (which is -ve since A is in the 4th quadrant)
= -5/13

someone can confirm whether mi or tamago is correct?

bonkysleuth SG

wishboy is correct. ^tamago^'s way of deriving the answer isn't wrong too. But he has to eliminate one of the signs (+ / -) since the answer isn't going to really be lying in all 4 quadrants.

By the way, towards the end where wishboy tried to find the answer for cos(pi/2 -A) = sin A, did you do so using the complementary angle formula? where cos x = sin (90 - x)? may i know why we can apply this formula here? how do you know it is a complementary angle without the question telling us so?

Thanks lots.

^tamago^ SG

opposite signs mean that if one is +ve, the other is -ve, and vice versa.

tan A = -5/12 (angle A falls in 2nd or 4th quadrant)

since they say tan A and cos A have opposite signs,
cos A is +ve (angle A falls in 1st or 4th quadrant)

so now u noe tat angle A is in the 4th quadrant

yours correct. misinterpret the word "can have" instead of "is", and forgot tan A is -ve so only left 2 quadrants. paiseh.