Given tan g = 5/12, find cos g:
5
tan g = ———
12
The tangent function is, by definition, the quotient between sine and cosine:
sin g 5
———— = ———
cos g 12
Product of them extremes = product of the means
12 · sin g = 5 · cos g
Square both sides:
(12 · sin g)² = (5 · cos g)²
12² · sin² g = 5² · cos² g
144 · sin² g = 25 · cos² g
But sin² g = 1 – cos² g. Substitute it for sin² g into the equation above, and you have
144 · (1 – cos² g) = 25 · cos² g
Multiply out the brackets, and then isolate cos² g:
144 – 144 · cos² g = 25 · cos² g
144 = 25 · cos² g + 144 · cos² g
144 = 169 · cos² g
Divide both sides by 169:
144
cos² g = ———
169
12²
cos² g = ———
13²
cos² g = (12/13)²
Now, take the square root of both sides:
cos g = ± √(12/13)²
12
cos g = ± ———
13
The sign of cos g depends on which quadrant the angle g lies. As tan g = 5/12, which is positive, then g lies either in the 1st or the 3rd quadrant:
• If g lies in the 1st quadrant, then
5
cos g > 0 ⇒ cos g = ——— ✔
13
• If g lies in the 3rd quadrant, then
5
cos g < 0 ⇒ cos g = – ——— ✔
13
I hope this helps. =)
Tags: <em>trigonometric relation tangent cosine sine tan cos sin trig trigonometry</em>
Answer:
2002
Step-by-step explanation:
The main topic of the question is compound interest.
If the percentage increase is 7.5%. Then the decimal multiplier would be 1.075. The 1 in front of the decimal represents the increase. 7.5 in decimal form is 0.075, so we just add the two together to get our decimal multiplier.
Now we do trial and error to see when we reach $700. After we get at least $700, we count how many times we multiplied $500 by the decimal multiplier and onwards to figure out the number of years it took and then add that to 1997. We add it to 1997 because the cost of the Freerange Wireless stock must have also been $500 at the end of 1997. The beginning of 1998 is the same as the end of 1997.
1) 500 x 1.075 = $537.50
2) 537.50 x 1.075 = $577.81
3) 577.81 x 1.075 = $621.15
4) 621.15 x 1.075 = $667.74
5) 667.74 x 1.075 = $717.8205
1997 + 5 = 2002
The value of Mira's stock will reach $700 by the end of 2002 because if we know that she used $500 at the beginning of 1998, that also means the cost of the Freerange Wireless stock was $500 at the end of 1997.
I hope this helps.
If we in the following equation y=x+7 assigns a value to x, the equation will give us a value for y. ... We could instead have assigned a value for y and solved the equation to find ... the independent variable, and the other variable is the dependent variable, ... A function is an equation that has only one answer for y for every x
