Lesson Example Discussion Quiz: Class Homework |
Example |
Title: Trigonometry Identities ( Pythagorean, reciporcal) |
Grade: 1300-a Lesson: S3-L3 |
Explanation: The best way to understand SAT-2 is by looking at some examples. Take turns and read each example for easy understanding. |
Examples:
If \$cot(α) = 5/12\$, where α is in quadrant II, find csc(α).
Step 1a
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To find csc(α), we first need to determine the sine of α since \$"csc"(α) = 1/("sin"(α))\$. In Quadrant II: \$"cot"(α) = "adjacent"/"opposite" = 5/12\$ |
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Explanation: In Quadrant II, apply the Pythagorean theorem to determine sinα, with adjacent side 5 and opposite side 12. |
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Step 1b
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Then use the Pythagorean theorem to find the hypotenuse: \$"c"^2 = "a"^2 + "b"^2\$ \$"c"^2 = 5^2 + 12^2\$ \$"c" = \sqrt(169)\$ c = 13 So, the hypotenuse c = 13. |
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Explanation: Utilize Pythagorean theorem for determining the length of the hypotenuse. |
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Step 1c
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Next, find the sine of α using the triangle: \$"sin"(α) = "opposite"/"hypotenuse" = 12/13\$ Finally, to find csc(α): \$"csc"(α) = 1/("sin"(α))\$ = \$1 /(12/13)\$ \$= 13/12\$ So, \$"csc"(α) = 13/12\$. |
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Explanation: Substitute hypotenuse in sin(α), simplify, then plug sin(α) in csc(α) formula to find csc(α). |
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