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## Algebra 2 Help: Pythagoras, Trigonometry, and Quadrants?

1) Simplify sine theta over square root of the quantity 1 minus sine squared theta.

sin(x) / sqrt( 1- sin^2(x) ) = sin(x) / sqrt( cos^2(x) ) = sin(x) / cos(x) = tan Θ

2) Is square root 1 minus sine squared theta = cos Θ true? If so, in which quadrants does angle Θ terminate?

It is true. The square root leads to a positive number. So the answer is in the quadrants where sine is positive. So (B)

False

True; quadrants I & IV

True; quadrants II & III

True; quadrants I & III

3) If sin Θ = 5 over 6, what are the values of cos Θ and tan Θ?

cos(x) = +/- sqrt( 1 – sin^2(x) ) = +/- sqrt( 1 – 25/36 ) =+/- sqrt( 11/36 ) = ± sqt(11) / 6

tan(x) = sin(x) / cos(x) = +/- 5 / sqrt(11)

cos Θ = ±11 over 36; tan Θ = ±1 over 11

cos Θ = ±square root 11 over 6; tan Θ = negative 1 over 11

cos Θ = ±11 over 6; tan Θ = negative 5 over 11

cos Θ = ±square root 11 over 6; tan Θ = ±5 square root 11 over 11

4) Simplify (1 − sin x)(1 + sin x). This is (a + b) (a – b) = a^2 – b^2

So this is 1 – cos^2(x) = sin^2(x)

1

cos2 x

sin2 x

tan2 x

5) If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ?

If 3 pi over 2 < Θ < 2π Then the signs of sinx and tanx are both negative.

cos(x) = sqrt(2)/2. So sin(x) = -sqrt(2)/2 and tan(x) = -1.

sin Θ = square root 2 over 2; tan Θ = −1

sin Θ = negative square root 2 over 2; tan Θ = 1

sin Θ = square root 2 over 2; tan Θ = negative square root 2

sin Θ = negative square root 2 over 2; tan Θ = −1

Simplify sine theta over square root of the quantity 1 minus sine… – In the problem ,theta is replaced by A. Find the distance between each pair of points (-1,7) (-6,6) How is the answer Square root of 26? 10 Which number can each term of the equation be multiplied by to eliminate the fractions before solvin = 2 + 1 m 3 4 oo 5.1) Simplify sine theta over square root of the quantity 1 minus sine squared theta. tan Θ. 2) Is square root 1 minus sine squared theta = cos Θ true? If so, in which quadrants does angle Θ terminate?simplify sine theta over square root of the quantity 1 minus sine squared theta. Watch0 watching·3 views.

Algebra 2 Help: Pythagoras, Trigonometry, and… | Yahoo Answers – Simplify the denominator. Tap for more steps… . Since both terms are perfect squares, factor using the difference of squares formulaHow to Simplify a Square Root. Simplifying a square root isn't as hard as it looks. Simplifying a square root just means factoring out any perfect squares from the radicand, moving them to the left of the radical symbol, and leaving the What is the square root of 18 minus the square root of 8?Answer with explanation In the problem ,theta is replaced by A.

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