Question

How to do it:
If theta and beta belong to Q1, and cot theta = 12/13, sin beta = √ 2/2, tan (theta + beta) is equal to:
a) - 20
b) 20
c) 25
d) - 25

Answer 1

is there a typo? is cot supposed to say cos?

Answer 2

it is cot

Answer 3

first you'll need to use the trig identities to find what theta and beta are

cot means cotangent and it = 1 / tan

sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent

opposite, adjacent, and hypotenuse all refer to the lengths of the sides of a right triangle

Answer 4

ok, how would you finish it? I am not sure how to go on

Answer 5

sorry I gotta sleep
I hope I can help on another day

Answer 6

sure, thank you

Answer 7

You could use the tangent of the sum of 2 angles formula
see http://www.intmath.com/analytic-trigonometry/2-sum-difference-angles.php

\[ \tan(a+b) = \frac{\tan(a)+ \tan(b)}{1 - \tan(a) \tan(b) } \]

you need to find the tangent of \( \theta\) and \( \beta \)
to use this formula.
in other words, if
\[ \cot(\theta)= \frac{12}{13} \]
what is \( \tan(\theta) \) ?

If you know
\[ \sin(\beta) = \frac{\sqrt{2}}{2} \]
what is \( \tan(\beta) \) ?
once you know those values, use the above formula

Answer 8

Thank you for your help