Evaluate the expression given that cosine a=4/5 with 0<a<pi/2 and sin b=-15/17 with 3pi/2< b<2pi
cos a = 4/5, and a is in quad I
Make your sketch and use Pythagoras:
x^2 + y^2 = r^2
16 + y^2 = 25
y^2 = 9
y = 3 in quad I
so sin a = 3/5
do the same for sin b = -15/17 , b in quad IV
x^2 + 225 = 289
x = +8 in quad IV
evaluate WHAT expression ?
but you now have both sines and cosines of both angles.
To evaluate the expression, we need to find the value of the expression itself. The expression can be written as cos(a) - 2sin(b).
Given that cos(a) = 4/5 and sin(b) = -15/17, we can substitute these values into the expression:
cos(a) - 2sin(b) = (4/5) - 2(-15/17)
To simplify this expression, we need to find a common denominator for the fractions. The least common denominator (LCD) of 5 and 17 is 85. Multiplying the numerators and denominators by the appropriate factors, we get:
cos(a) - 2sin(b) = (4/5) - 2(-15/17) = (4/5) - (2*-15/17*5) = 4/5 + 30/85
Now, we add the numerators:
4 + 30 = 34
And keep the denominator the same:
34/85
Therefore, the value of the expression cos(a) - 2sin(b) is 34/85.