Date | May 2014 | Marks available | 2 | Reference code | 14M.1.sl.TZ2.1 |
Level | SL only | Paper | 1 | Time zone | TZ2 |
Command term | Show that | Question number | 1 | Adapted from | N/A |
Question
The following diagram shows a right-angled triangle, ABC, where sinA=513.
Show that cosA=1213.
Find cos2A.
Markscheme
METHOD 1
approach involving Pythagoras’ theorem (M1)
eg 52+x2=132, labelling correct sides on triangle
finding third side is 12 (may be seen on diagram) A1
cosA=1213 AG N0
METHOD 2
approach involving sin2θ+cos2θ=1 (M1)
eg (513)2+cos2θ=1, x2+25169=1
correct working A1
eg cos2θ=144169
cosA=1213 AG N0
[2 marks]
correct substitution into cos2θ (A1)
eg 1−2(513)2, 2(1213)2−1, (1213)2−(513)2
correct working (A1)
eg 1−50169, 288169−1, 144169−25169
cos2A=119169 A1 N2
[3 marks]