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Dave C.

Private Math tutor with 18 years experience

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Pre-Calculus

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Question:

What is the reference angle of a 240 degree angle on the unit circle? What is the sign of the cosine of this angle? What is the sign of the sine of this angle?

Dave C.

Answer:

Moving counterclockwise from zero, 240 degrees is 60 degrees past 180, terminating in the third quadrant. So the reference angle (always formed using the x-axis) is 60 degrees. Since both X and Y are Negative in the third (III) quadrant, both sine and cosine are Negative.

Trigonometry

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Question:

Sam's cat, Roxy, has always slept on a little bed which is elevated 3 feet off the floor. This perch gives her a great view of what's happening outside the window. But Roxy is getting old and can longer leap up to her bed like she used to, so Sam wants to build her a ramp. If the ramp is to incline at an angle of 20 degrees, what length ramp would be needed?

Dave C.

Answer:

Draw a right triangle. Label the 2 known angles, 90 and 20 degrees. The 3rd angle must be 180 - 90 - 20 = 70 degrees. The vertical leg would be the distance from the floor to the bed, so label that 3 feet. Where that leg and the floor meet is where the right angle is. The length of the ramp would be the hypotenuse in this case. So with one known side length and all the angles known, you can use the Law of Sines. The 3 foot side is opposite the 20 degree angle; the hypotenuse is opposite the right angle (always). So set up: 3/sin20 = x/sin90. When you solve this you find that the ramp needs to be about 8.8 feet long.

Algebra

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Question:

An amusement park charges each patron a $20 entry fee, plus $5 for every whole hour they stay which is paid upon leaving. a) Write an equation in y=mx + b form to model this situation. b) What is the meaning of the y-intercept in this case?

Dave C.

Answer:

a) The equation would be y = 5x + 20 b) The y-intercept, which is 20, would be what it cost a patron who entered the park but stayed less than an hour. That is, when x = zero or any value less than 1.

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