# Tutor profile: Henry H.

## Questions

### Subject: Pre-Calculus

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

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

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

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

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?

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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