Hi:) anyone able to explain why at the TOP , they said cOS (180-0) = -cos 0
but for example 2 ,
cOS 0 = - cOS (180 - 0) ?

cos (180° -θ)= -cosθ

-cos θ= cos (180° -θ)

(-cos θ)(-1)= -cos (180° -θ) (multiply by -1 on both sides)

cosθ= -cos (180° -θ) (simplify)

Note that the question is cos 154° not -cos 154°.

See attached picture:

Draw a line at 154° (dont need to be exactly 154°- just between 90° and 180°) and label the reference angle. The reference angle lies in the 2nd quadrant. In the 2nd quadrant, only the sine of an angle is positive. All the others are negative (cosine, tangent).

Reference angle= 180° -154°= 26°

Thus cos 154°= -cos 26°

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.

a

explanation: