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# Tutor profile: Henry H.

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Henry H.
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## Questions

### Subject:Pre-Calculus

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Question:

Referencing the Unit Circle, if sin(t)= 1/2 and cos(t) is a positive value, what does tan(t)=?

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Henry H.

In the Unit Circle (0-2pi), the cartesian coordinates of (x,y) can be represented based on their reference angle and trigonometric function as (cos(t), sin(t)). The reference angle where sin(t)=y=1/2 is either pi/4 or 3pi/4 The reference angle where cos(t) is positive is in Quadrant I or IV This leave the only viable reference angle as pi/4, where sin(t)=1/2 and cos(t)=1/2 The value of tan(t)=sin(t)/cos(t). Therefore, tan(t)=(1/2)/(1/2)= 1

### Subject:Basic Math

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Question:

Using the Order of Operations (PEMDAS), What is the answer to this equation? 4+6*(8/2+2)=?

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Henry H.

STEP 1 P-Parentheses (8/2+2) D-Division (8/2+2) = (4+2) A-Addition (4+2) = (6) STEP 2 Replace parentheses with calculated value 4+6*(8/2+2) = 4+6*(6) M-Multiplication 4+6*(6) = 4+36 A- Addition 4+36 = 40 ANSWER: 4+6*(8/2+2) = 40

### Subject:Algebra

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Question:

In one year Samuel sells \$5000 worth of gems at \$5 each. How many more gems must Samuel sell if he want to have a 20% increase in sales by the next year?

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Henry H.

The question can be approached in many ways, but it is important to first identify the variables you are working with. The known values include Year 1 Sales: \$5000, Cost of Gems: \$5, and the Increase in Sales: 20%. The question is asking for the difference of gems sold between Year 1 and 2 to achieve an increase of 20% in sales. This can be done in two ways. Method 1: Multiply the Year 1 Sales(\$5000) by 120% to simulate an increase in 20% 5000 * 1.2 = 6000 Divide the total by Cost per Gem (\$5) to identify number of gems needed to be sold 6000 / 5 = 1200 Subtract the number of gems sold from Year 2 by Year 1 gems (\$5000/\$5) 1200 - (5000/5) = 200 200 more gems need to be sold next year to increase profit by 20% Method 2: (much faster) Calculate how many gems were sold in Year 1 \$5000 total / \$5 per gem = 1000 gems Increase that total by 20% then find the difference 1000 * 1.2 = 1200 1200 - 1000 = 200 200 more gems need to be sold next year to increase profit by 20%

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