evaluate the trigonometric functions by memory or by constructing appropriate triangles for the given special angles.
a) csc 30 degrees
b) sin pi/4 = sqrt2 / 2
I just do not know how to find csc 30 degrees.
You should know that cscx = 1/sinx
so
csc 30
= 1/sin 30
= 1/(1/2) = 2
To find the value of csc 30 degrees, we need to first understand what csc represents. The cosecant (csc) function is the reciprocal of the sine (sin) function. So, csc x is equal to 1/sin x.
For special angles such as 30 degrees, it is helpful to rely on knowledge of common trigonometric values and the unit circle.
Let's proceed step by step to find csc 30 degrees:
Step 1: Recall the values of sin for special angles:
- sin 0 degrees = 0
- sin 30 degrees = 1/2
- sin 45 degrees = sqrt(2)/2
- sin 60 degrees = sqrt(3)/2
- sin 90 degrees = 1
Step 2: Find the value of sin 30 degrees, which is 1/2.
Step 3: Take the reciprocal of sin 30 degrees to find csc 30 degrees:
- csc 30 degrees = 1/(1/2)
- csc 30 degrees = 2/1
- csc 30 degrees = 2
Therefore, csc 30 degrees is equal to 2.
You can also construct an appropriate triangle for the 30-degree angle, where the opposite side is 1 and the hypotenuse is 2. Then, using the Pythagorean theorem, you can find the adjacent side, which will be sqrt(3). Finally, you can use the definition of csc as the reciprocal of sin to obtain the value of csc 30 degrees.