Cos180* - Sin90* + Cot45* - Csc30* - Sec240* - Tan315*
How do I do this?
all these are standard angles for which you should know the trig ratios
cos 180 = -1 , look at the cosine curve
sin 90 = 1 , look at the sine curve
cot 45 = 1/tan45 = 1/1 = 1 , look at your 45-45-90 triangle
csc 30 = 1/sin30 = 1/(1/2) = 2 , look at the 30-60-90 triangle
sec 240 = 1/cos240 = - 1/cos60
= -1/(1/2) = -2 , using the CAST rule and 30-60-90 triangle
tan 135 = -tan45 = -1
now just add them up
these are all standard angles you should know by heart. It will save you a lot of trouble working them out all the time.
-1 - 1 + 1 - 2 + 2 + 1 = 0
It also involves knowing the signs of the trig functions in the various quadrants, and how to figure the reference angle.
Also, lose the capitalization.
To simplify this expression, we can use the trigonometric identities and the unit circle. Let's break it down step by step:
1. Cosine of 180 degrees (°): The cosine of 180° is -1.
2. Sine of 90 degrees (°): The sine of 90° is 1.
3. Cotangent of 45 degrees (°): The cotangent of an angle is equal to the reciprocal of the tangent of the same angle. The tangent of 45° is 1, so the cotangent of 45° is also 1.
4. Cosecant of 30 degrees (°): The cosecant of an angle is equal to the reciprocal of the sine of the same angle. The sine of 30° is 1/2, so the cosecant of 30° is 2.
5. Secant of 240 degrees (°): The secant of an angle is equal to the reciprocal of the cosine of the same angle. To find the cosine of 240°, we can use the unit circle. The cosine of 240° is -1/2, so the secant of 240° is -2.
6. Tangent of 315 degrees (°): The tangent of 315° can be found using the unit circle. The tangent of 315° is -1.
Now, let's substitute these values into the original expression:
-1 - 1 + 1 - 2 - (-1) - 1
Simplifying further:
-1 - 1 + 1 - 2 + 1 - 1
Combining like terms:
-4
Therefore, the value of the expression is -4.