Aaron
Can you solve the following equation (quote the value of x,y and t to 3 sig figs)
((i have changed figures so that i can work through my own example))
x2 + x – 6 = 0
5y2 +19y = 3
10cos2 t + 3cos t = 4
Hi Aaron,
Let me do the third problem. First I will write x = cos t to make this problem look like the first two. The equation then becomes
10 x2 + 3 x - 4 = 0
To factor this quadratic you need to consider the divisors of 10 and 4. The divisors of 10 are 1, 5 and 10 and the divisors of 4 are 1, 2 and 4. If you try the possible combinations you will see that
10 x2 + 3 x - 4 = (5 x + 4)(2 x - 1) = 0
Thus either x = - 4/5 or x = 1/2. But x is cos t so either
cos t = - 4/5 or cos t = 1/2.
If cos t = 1/2 and t is in the first quadrant then t is 60 degrees. If t -s - 4/5 then you can use your calculator to find t.
Penny