Tutor profile: Sabahat G.
Using trig identities, simplify the following equation cos^2(x) - tan^2(x) +sin^2(x) + sec^2(x)
Remember that the basic trig identities are cos^2(x) + sin^2(x) = 1 1 + tan^2(x) = sec^2(x) 1 + cot^2(x) = csc^2(x) Start to look for the identities within the expression. What do you see? There is a cos^2(x) and a sin^2(x). Does that resemble on the basic identities? Yes! The first one. It doesn't matter if the terms aren't beside each other. We can rearrange the expression so cos^2(x) + sin^2(x) are beside each other. Based on the identity, what does that equal? It equals 1. That leaves sec^2(x) - tan^2 (x). We don't see that above, but if we rearrange the second identity, and subtract tan^2(x) from both sides, we would get sec^2(x) - tan^2 (x) = 1. This gives us 1 + 1 = 2.
Add the following 3/4 + 5/7
The answer to this is NOT 8/11! Remember, in order to add or subtract fractions, we need a common denominator. What is the LCF between 4 and 7? 28. So we need to change both denominators to 28. But we can't just change the denominator. If we do something to the bottom, we need to do the SAME thing to the top to make sure we are not changing the fraction. Since 4*7 = 28, we would multiply both the top and bottom of the first fraction by 7. Likewise, 7*4 = 28, so we would multiply both the top and bottom of the second fraction by 4. so we would get 12/28 + 20/28. Now that there is a common denominator, we write that same denominator, and combine the numerators giving us an answer of 32/28 which would reduce to 8/7 or 1 and 1/7.
What is the vertex form of the following equation: y = x^2+6x+5?
In order to find the vertex form for the equation(which is currently in standard form), write the left side of the equation = 0. x^2+6x+5 = 0. Then move the constant to the other side which gives you x^2+6x = -5. Then we need to complete the square. The steps for this are 1. divide the b value by 2 2. square the b value 3. add it to both sides(to "balance" the equation). Remember that the b value is the coefficient of the x. This gives them x^2+6x+9= -5+9. Then factor the right side(show shortcut which is (x+b/2)^2. So you would get (x+3)^2 = 4. Then bring the constant from the left side back over to the right. This gives you y = (x+3)^2-4. The vertex is (-3, -4)
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