evaluate each expression. write your answer in exact form. csc 150 degrees
There are a few ways to approach this problem, but one possible method is to use the definition of the cosecant function:
cscθ = 1/sinθ
where θ is an angle in radians or degrees. In this case, we want to find csc 150 degrees, so we can substitute 150 degrees for θ and use the sine of its reference angle, which is 30 degrees:
csc 150 degrees = 1/sin 30 degrees
We can evaluate sin 30 degrees exactly using the special right triangle with angles 30-60-90:
sin 30 degrees = opposite/hypotenuse = 1/2
Therefore, we have:
csc 150 degrees = 1/sin 30 degrees = 1/(1/2) = 2
The exact value of csc 150 degrees is 2.
no words just a series of what you did to get your answer
csc 150 degrees = 1/sin 30 degrees
sin 30 degrees = 1/2
csc 150 degrees = 1/(1/2)
csc 150 degrees = 2
thank you!!
You're welcome! Feel free to ask if you have any more questions.
To evaluate the expression csc 150 degrees, we first need to understand that csc (cosecant) is the reciprocal of the sine function.
The sine of 150 degrees is:
sin 150° = sin (180° - 30°)
Since sin (180° - x) = sin x, we have:
sin 150° = sin 30°
The sine of 30 degrees is:
sin 30° = 1/2
Now, the cosecant function is the reciprocal of the sine function, so:
csc 150° = 1 / sin 150° = 1 / (1/2) = 2
Therefore, the exact value of csc 150 degrees is 2.
To evaluate the expression csc 150 degrees, we need to find the cosecant of the angle 150 degrees.
The cosecant (csc) of an angle is the ratio of the hypotenuse to the length of the side opposite the angle in a right triangle.
To find the exact value of csc 150 degrees, we can use the unit circle or reference angles.
Step 1: Reference angle
Since 150 degrees is greater than 90 degrees but less than 180 degrees, we need to find the reference angle in the first quadrant.
The reference angle is the acute angle formed between the terminal side of the angle and the x-axis. In this case, the reference angle is 30 degrees (180 degrees - 150 degrees).
Step 2: Unit Circle
We know that the sine function is equal to the length of the y-coordinate on the unit circle. To find the csc 150 degrees, we need to find the reciprocal of the sine of the reference angle.
The sine of 30 degrees is 1/2, so the csc 150 degrees is 1 / (1/2) = 2.
Therefore, the exact value of csc 150 degrees is 2.