Draw a right-angled triangle ABC where B is 90 deg, A is theta. cot(theta)=AB/BC=7. AC=sqrt(7^2+1)=5sqrt(2). AB=7, BC=1.

sin(theta)=BC/AC=1/5sqrt(2)=0.2sqrt(2)/2=0.1sqrt(2)=0.1414. cos(theta)=7/5sqrt(2)=1.4sqrt(2)/2=0.7sqrt(2)=0.9899.

sec(theta)=1/cos(theta)=5sqrt(2)/7=1.0102. These are all approximate values and apply to quadrant 1. cot(theta)=7/1 in quadrant 1, or -7/-1 in quadrant 3. In this quadrant sin, cos, sec are all negative, so sin(theta)=-0.1414, cos(theta)=-0.9899, sec(theta)=-1.0102 in QIII, and 0.1414, 0.9899, 1.0102 in QI.

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