I am very confused about the concepts of..
sin è = sin(180 - è)
sin (180 + è)= -sinè
tan (180 - è) = -tanè
and how the final answer was found in this problem...
Find cos 510:
cos510=cos(540-30)
=-cos30
=-s.r3/2
i don't understand how we went from -cos 30 to -s.r3/2 ?
To understand how we arrived at the final answer of -√3/2, let's break down the steps:
1. We are given the problem to find cos 510.
2. One way to approach this is by using the angle subtraction identity for cosine: cos (a - b) = cos a * cos b + sin a * sin b.
3. In this case, we want to find cos 510, which can be written as cos (540 - 30).
4. Using the angle subtraction identity, we can rewrite this as: cos 540 * cos 30 + sin 540 * sin 30.
5. Since cos 540 = -1 and sin 540 = 0, we can substitute these values in: -1 * cos 30 + 0 * sin 30.
6. Therefore, our equation becomes: -cos 30.
7. Now, we need to evaluate cos 30. We can use the unit circle or trigonometric ratios to find this value.
8. Based on the values obtained from the unit circle or known trigonometric ratios, we get cos 30 = √3/2.
9. Finally, since our original equation was -cos 30, we have: -√3/2 as the final answer.
So, the final answer of -√3/2 is obtained through the process of evaluating the trigonometric function cos 30 and applying the angle subtraction identity to simplify the expression.