**High School Number Sense Lesson 87: Trigonometric Values**

I'll be honest...I've been putting off covering this particular concept because of its complexity. I have always wanted to approach this blog with "baby steps," where each new idea builds upon previous ideas, but without too much of a mental stretch. Today I'm going to have to rely on some outside help, because I feel like I have nothing unique to offer in this arena.

This concept appeared

**8 times**on high school tests this year, with a median placement at

**question # 65**.

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Probably the best place to start for this topic is on Khan Academy's website, specifically with

**this**post. Please take the time to review it...don't worry, I'll wait!

Welcome back! Another very helpful resource is

**Bryant Heath's**Number Sense Tricks Manual, which is found

**here**. The specific lesson for today's concept is section

**2.2.11**, which begins on

**page 86**of the document. (This will soon be updated, so I'll try to remember to update this information when that happens).

**Example 1: sin(150°) = ___**

- 150° is in Quadrant II, and its reference angle is (180 - 150) =
**30°** - sin(30°) =
**1/2**

**Example 2: tan(405°) = ___**

- To find the reference angle, subtract 360° to get
**45°** - tan(45°) =
**1**

**Example 3: cos(-300°) = ___**

- Add 360° to get the reference angle:
**60°** - cos 60° =
**1/2**

**Example 4: cos(2π/3) = ___**

- 2π/3 =
**120°** - 120° is in Quadrant II, and its reference angle is (180 - 120) = 60°
- cos(60)° = 1/2, but since 120° is left of the y-axis, its cosine is negative. The answer is
**- 1/2**.

**Example 5: csc(5π/6) = ___**

- 5π/6 =
**150°** - 150
**°**is in Quadrant II, and its reference angle is (180 - 150) =**30°** - csc(30
**°**) = 1/sin(30**°**) = 1/(1/2) =**2**

**Up Next for High School: Integral**