if sin23=p,write down the following in terms of P
*cos113
*cos23
*sin46
so i draw the diagram an solve for x in terms of P an got 1-p
so i don't know how to apply cos113and sin46 in terms of 23 or P
but *cos 23 i wrote it as> 1-p/1 wch is 1-p
To find *cos113 in terms of P, we can use the identity cos(180° - x) = -cos(x). Since 113° is the complement of 180° - 23°, we can rewrite it as cos(180° - 23°). Thus, *cos113 = -cos(23°) = -P.
Similarly, to find *sin46 in terms of P, we can use the identity sin(180° - x) = sin(x). Since 46° is the complement of 180° - 134°, we can rewrite it as sin(134°). Thus, *sin46 = sin(134°) = P.
Hope this helps! Let me know if you have any other questions.
To write down the following trigonometric values in terms of P:
1. *cos113:
To find cos113, we need to use the fact that cos(x) = sin(90 - x) and the given value of sin23 = P.
cos113 = sin(90 - 113) = sin(-23)
Since sin function is an odd function, sin(-23) = -sin(23) = -P
Therefore, *cos113 = -P
2. *cos23:
You correctly wrote *cos23 as (1 - P).
3. sin46:
To find sin46, we can use the fact that sin(x) = cos(90 - x). Since we know the value of sin23 = P, we can find cos23 as follows:
cos23 = sin(90 - 23) = sin67
Now, to find sin46, we can use the fact that sin(x) = cos(90 - x):
sin46 = cos(90 - 46) = cos44
Since cos44 is not directly related to P or 23, we cannot simplify it further using the given information.
Therefore, sin46 = cos44.
since sin^2 + cos^2 = 1,
cos(23) = √(1-p^2)
cos(113) = cos(23+90) = cos(23)cos(90) - sin(23)sin(90) = -p
sin(46) = 2sin(23)cos(23) = 2p√(1-p^2)
Time to review your basic sum/double-angle formulas